Question 1

Write down the values of:
$(5+\sqrt3)^2$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$22-10\sqrt{3}$
$28+10\sqrt{3}$
$22+10\sqrt{3}$
$28-10\sqrt{3}$

Answer

Correct Option: B

Question 2

Write down the values of:
$(\sqrt5+\sqrt6)^2$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\sqrt5+\sqrt6+\sqrt{30}$
$11+2\sqrt{30}$
$11+\sqrt{30}$
$\sqrt{11}+60$

Answer

Correct Option: B

Question 3

Expand $(5-6\sqrt3)^2$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$133+30\sqrt3$
$133-60\sqrt3$
$83-60\sqrt3$
$83+30\sqrt3$

Answer

Correct Option: B

Question 4

Write down the values of:
$4(\sqrt6-3)^2$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$30-24\sqrt{6}$
$15-6\sqrt{6}$
$15+12\sqrt{6}$
$60-24\sqrt{6}$

Answer

Correct Option: D

Question 5

Write down the values of:
$(3+2\sqrt5)^2$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$29+12\sqrt{5}$
$29+6\sqrt{5}$
$19-12\sqrt{5}$
$29-6\sqrt{5}$

Answer

Correct Option: A

Question 6

Evaluate: ${(5^2+12^2)^{\frac{1}{2}}}3$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$54$
$34$
$39$
$59$

Answer

Correct Option: C

Question 7

Find the square of $2a+b$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$4a^{2} + 4ab + b^{2}$
$a^{2} + ab + b^{3}$
$4a^{2} + ab + b^{2}$
$4a^{2} + 4ab - b^{2}$

Answer

Correct Option: A

Question 8

Find the square of $3a + 7b$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$9a^{2} + 42ab + 49b^{2}$
$9a^{2} + 40ab + 49b^{2}$
$18a^{2} + 42ab + 98b^{2}$
$18a^{2} + 40ab + 98b^{2}$

Answer

Correct Option: A

Question 9

$\sqrt{3\,+\,2\,\sqrt{2}}\,-\,\sqrt{3\,-\,2\,\sqrt{2}}$ is equal to

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$2$
$1$
$2\sqrt{2}$
$\sqrt{6}$

Answer

Correct Option: A

Question 10

Use identities to evaluate $\displaystyle \left ( 998 \right )^{2}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\displaystyle 9,96,004$
$\displaystyle 9,16,004$
$\displaystyle 9,96,104$
$\displaystyle 9,96,324$

Answer

Correct Option: A

Question 11

Use identities to evaluate $\displaystyle \left ( 97 \right )^{2}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\displaystyle 9,109$
$\displaystyle 9,409$
$\displaystyle 9,909$
$\displaystyle 9,209$

Answer

Correct Option: B

Question 12

Use identities to evaluate $\displaystyle \left ( 101 \right )^{2}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\displaystyle 10,301$
$\displaystyle 12,301$
$\displaystyle 10,201$
$\displaystyle 12,201$

Answer

Correct Option: C

Question 13

Use identities to evaluate :$\displaystyle \left ( 502 \right )^{2}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\displaystyle 1,62,004$
$\displaystyle 1,22,004$
$\displaystyle 2,12,004$
$\displaystyle 2,52,004$

Answer

Correct Option: D

Question 14

The simplified value of $\displaystyle \left ( \sqrt{3}+1 \right )^{2}-2\left ( 2+\sqrt{3} \right )$ is

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

2
-1
1
0

Answer

Correct Option: D

Question 15

Evaluate the following

$(97)^{2}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$9409$
$9049$
$9949$
$4949$

Answer

Correct Option: A

Question 16

If $3x - \dfrac {1}{2x} = 6$, then the value of $9x^{2} + \dfrac {1}{4x^{2}}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$36$
$33$
$30$
$39$

Answer

Correct Option: D

Question 17

If $x - \dfrac {1}{x} = \sqrt {6}$, then $x^{2} + \dfrac {1}{x^{2}}$ is ________.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$2$
$4$
$6$
$8$

Answer

Correct Option: D

Question 18

If $2l - 3m = -1$ and $lm = 20$, then the value of $4l^{2} + 9m^{2}$ is ________.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$239$
$240$
$241$
$361$

Answer

Correct Option: C

Question 19

On simplification the product of given expression $\left (x - \dfrac {1}{x}\right )\left (x + \dfrac {1}{x}\right )\left (x^{2} + \dfrac {1}{x^{2}}\right )$ is ________.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$x^{3} - \dfrac {1}{x^{3}}$
$x^{3} + \dfrac {1}{x^{3}}$
$x^{4} - \dfrac {1}{x^{4}}$
$x^{4} + \dfrac {1}{x^{4}}$

Answer

Correct Option: C

Question 20

Find the missing term in the following problem.
$\left (\dfrac {3x}{4} - \dfrac {4y}{3}\right )^{2} = \dfrac {9x^{2}}{16} + \dfrac {16y^{2}}{9} + ?$.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$2xy$
$-2xy$
$12xy$
$-12xy$

Answer

Correct Option: B

Question 21

$(9p - 5q)^{2} + 180 pq$ is equivalent to _______.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$(5p + 9q)^{2}$
$(5p - 9q)^{2}$
$(9p + 5q)^{2}$
$(9p - 5q)^{2}$

Answer

Correct Option: C

Question 22

If $\sqrt{\left(12+\sqrt{12+\sqrt{12+....}}\right)}=x$, then the value of x is ____________.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$3$
$4$
$6$
Greater than $6$

Answer

Correct Option: B

Question 23

$\sqrt { 3+2\sqrt { 2 } } +\sqrt { 3-2\sqrt { 2 } } =...$ ?

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$2+2\sqrt {2}$
$2\sqrt {2}$
$1$
$0$

Answer

Correct Option: B

Question 24

if $y = 500{e^{7x}} + 600{e^{-7x}}$ . Then $\dfrac{{d^2y}}{dx^2} = 49y$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

True
False

Answer

Correct Option: A

Question 25

Evaluate each of the following using identities :
i) $(399)^2$
ii) $(0.98)^2$
iii) $991 \times 1009$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

i) 159876
ii) 0.91

iii) 876590
i) 135879
ii) 0.87

iii) 896750
i) 159201
ii) 0.9604

iii) 999919
i) 138760
ii) 0.9

iii) 999999

Answer

Correct Option: C

Question 26

If $a + b + c = 9$ and $ab + bc + ca = 26$, then the value of $a^2 + b^2 + c^2$ is

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$29$
$52$
$81$
None

Answer

Correct Option: A

Question 27

If $x^{2}+2(a-1)x+a+5=0$ has real roots to the interval $(1,3)$, then complete set of value of $'a'$ is

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\left(-\infty,-\dfrac {8}{7}\right)$
$(4,\infty)$
$\left(-\infty,-\dfrac {48}{3}\right)$
$a\ \epsilon \left(-\dfrac {8}{7},-1 \right]$

Answer

Correct Option: D

Question 28

Find the square of $83$ without actual multiplication.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$6880$
$3881$
$3889$
$6889$

Answer

Correct Option: D

Question 29

If $x^{2}+\dfrac{1}{^{x^2}}=18$, then the value of $\left(x+\dfrac{1}{x}\right)$ is ?

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$1$
$3$
$\sqrt {20}$
$6$

Answer

Correct Option: C

Question 30

If $5a\sqrt{b}-\dfrac{3}{2b\sqrt{a}}=12$ and $a=8b$, then the value of $25a^{2}b+\dfrac{9}{4ab^{2}}$ is ?

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$144-15\sqrt{8}$
$144+15\sqrt{8}$
$15\sqrt{8}-144$
$-15\sqrt{8}-144$

Answer

Correct Option: B

Question 31

If $x+\cfrac{1}{x}=5$, then ${x}^{2}+\cfrac{1}{{x}^{2}}$ is equal to

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$25$
$10$
$23$
$27$

Answer

Correct Option: C

Question 32

If ${x}^{2}+\cfrac{1}{{x}^{2}}=102$, then $x-\cfrac{1}{x}$ is equal to

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$8$
$10$
$12$
$13$

Answer

Correct Option: B

Question 33

If ${x}^{3}+\cfrac{1}{{x}^{3}}=110$, then $x+\cfrac{1}{x}$ is equal to

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$5$
$10$
$15$
None of these

Answer

Correct Option: A

Question 34

If $x+\cfrac{1}{x}=4$, then ${x}^{4}+\cfrac{1}{{x}^{4}}$ is equal to

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$196$
$194$
$192$
$190$

Answer

Correct Option: B

Question 35

Evaluate $\displaystyle \left ( \frac{2x}{7} - \frac{7y}{4} \right )^{2}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\displaystyle \frac{x^{2}}{49} + \frac{17y^{2}}{16} - xy$
$\displaystyle \frac{4x^{2}}{49} + \frac{49y^{2}}{16} - xy$
$\displaystyle \frac{4x^{2}}{9} + \frac{49y^{2}}{4} - xy$
$\displaystyle \frac{x^{2}}{13} + \frac{49y^{2}}{13} - xy$

Answer

Correct Option: B

Question 36

Evaluate $\displaystyle \left ( \frac{7}{8}x + \frac{4}{5}y \right ) ^{2}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\displaystyle \frac{49}{64}x^{2} + \frac{16}{25}y^{3} + \frac{7}{5}xy$
$\displaystyle \frac{78}{32}x^{2} + \frac{16}{25}y^{2} + \frac{1}{5}xy$
$\displaystyle \frac{49}{64}x^{2} + \frac{16}{25}y^{2} + \frac{7}{5}xy$
$\displaystyle \frac{78}{32}x^{2} + \frac{16}{25}y^{2} + \frac{1}{6}xy$

Answer

Correct Option: C

Question 37

Find square of the following expression

$\displaystyle 3a - 4b$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\displaystyle a^{2} - 24ab + 48b^{2}$
$\displaystyle 9a^{2} - 4ab + 48b^{2}$
$\displaystyle 9a^{2} - 24ab + 16b^{2}$
$\displaystyle a^{2} - 24ab + 16b^{2}$

Answer

Correct Option: C

Question 38

Find square of the following expression

$\displaystyle \frac{3a}{2b} - \dfrac{2b}{3a}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\displaystyle \dfrac{9a^{2}}{4b^{2}} - 2 + \dfrac{b^{2}}{a^{2}}$
$\displaystyle \dfrac{9a^{2}}{4b^{2}} + 2 + \dfrac{4b^{2}}{9a^{2}}$
$\displaystyle \dfrac{a^{2}}{4b^{2}} - 2 + \dfrac{4b^{2}}{9a^{2}}$
$\displaystyle \dfrac{9a^{2}}{4b^{2}} - 2 + \dfrac{4b^{2}}{9a^{2}}$

Answer

Correct Option: D

Question 39

Find the square of $\displaystyle a + 2b + c$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\displaystyle a^{2} + b^{2} + c^{2} + ab + bc + ac$
$\displaystyle a^{2} + 4b^{2} + c^{2} + 4ab + 4bc + 2ac$
$\displaystyle a^{3} + 4b^{3} + c^{3} + 8ab + 8bc + 8ac$
$\displaystyle a^{3} + b^{3} + c^{3} + 4ab + 4bc + 2ac$

Answer

Correct Option: B

Question 40

Find the square of $\displaystyle 2a - b - 3c$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\displaystyle 4a^{2} + b^{2} + 9c^{2} - 4ab + 6bc - 12ca$
$\displaystyle a^{3} + b^{3} + c^{2} - 4ab + 6bc - ca$
$\displaystyle a^{2} + b^{2} - c^{2} - 4ab + 6bc - 2ca$
$\displaystyle 4a^{3} + b^{3} + 9c^{2} - 4ab - 6bc - 12ca$

Answer

Correct Option: A

Question 41

Evaluate :

$\displaystyle \left ( \frac{2x}{5} + \frac{3y}{4} - \frac{4z}{7} \right )^{2}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\displaystyle \frac{x^{2}}{25} + \frac{9y^{2}}{16} + \frac{z^{2}}{49} + \frac{3}{5} xy - \frac{6}{7}yz - \frac{16}{35}zx$
$\displaystyle \frac{4x^{2}}{25} + \frac{9y^{2}}{16} + \frac{16z^{2}}{49} + \frac{1}{5} xy - \frac{6}{3}yz - \frac{36}{35}zx$
$\displaystyle \frac{x^{2}}{25} + \frac{9y^{2}}{16} + \frac{5z^{2}}{49} + \frac{3}{5} xy - \frac{6}{7}yz - \frac{16}{35}zx$
$\displaystyle \frac{4x^{2}}{25} + \frac{9y^{2}}{16} + \frac{16z^{2}}{49} + \frac{3}{5} xy - \frac{6}{7}yz - \frac{16}{35}zx$

Answer

Correct Option: D

Question 42

Find the squares of the following numbers without actual multiplication:
$49$
$52$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$2441; 2704$
$2401; 2784$
$2401; 2704$
$2441; 2784$

Answer

Correct Option: C

Question 43

Find the square of $43$ without multiplication.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$2401$
$4801$
$1842$
$1849$

Answer

Correct Option: D

Question 44

Find the square of $125$.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$84113$
$48000$
$15625$
$84920$

Answer

Correct Option: C

Question 45

Without doing multiplication, find the square of $29.$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$841$
$480$
$742$
$849$

Answer

Correct Option: A

Question 46

Without actual finding the square of the numbers, find the value of $120^2 - 119^2$.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$239$
$240$
$238$
$237$

Answer

Correct Option: A

Question 47

Without actual finding the square of the numbers, find the value of $36^2 - 35^2$.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$70$
$71$
$72$
$73$

Answer

Correct Option: B

Question 48

Evaluate the following

$(0.98)^{2}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$0.9664$
$0.9604$
$0.9864$
$0.9964$

Answer

Correct Option: B

Question 49

A factor of $(3x^{4} - 12y^{4})$ is _________.

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$3$
$x^{2} - 2y^{2}$
$x^{2} + 2y^{2}$
All of these

Answer

Correct Option: A

Question 50

Find the square of the following number without multiplication.

46

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

2116
2002
2424
1988

Answer

Correct Option: A

Question 51

If sin$\theta -cosec \theta =\sqrt{5},$ then the value of sin $\theta + cosec \theta$ is:

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$\sqrt{3}$
1
3
9

Answer

Correct Option: C

Question 52

If $a+b+c=6$ and $ ab+bc+ca = 11 $

Find $\left( { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 } \right)$ ?

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$14$
$25$
$36$
$47$

Answer

Correct Option: A

Question 53

Evaluating the following :
$(3+\sqrt{2})^{5}-(3-\sqrt{2})^{5}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$1718\sqrt 3$
$1718\sqrt 2$
$1178\sqrt 3$
$1178\sqrt 2$

Answer

Correct Option: D

Question 54

Evaluating the following :
$(1+2\sqrt{x})^{5}+(1-2\sqrt{x})^{5}$

maths squares and square roots finding the square of a number finding square of a number patterns in square numbers

$2(1+40x^2+80x)$
$2(1-40x+81x^2)$
$2(1+40x+80x^2)$
None of these

Answer

Correct Option: C

Description: finding the square of a number
Number of Questions: 55
Created by: Avatara Chahal
Tags: square and square roots maths squares and square roots squares, square roots, cubes, cube roots square roots and cube roots

Finding the square of a number - class-VIII

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