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Square and square roots using vedic mathematics - class-X

Description: square and square roots using vedic mathematics
Number of Questions: 48
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Find the square of $725$ using Vedic Mathematics.

  1. $543625$

  2. $525625$

  3. $562625$

  4. None of these


Correct Option: B
Explanation:

Next number of 72 is 73
Square of 725 = (72 × 73)25 = 525625

Find the square of $125$ using Vedic Mathematics.

  1. $15625$

  2. $15325$

  3. $12225$

  4. None of these


Correct Option: A
Explanation:

Next number of 12 is 13.
Square of 125 = (12 × 13)25
= 15625

Using vedic mathematics term "Ekadhik", find the value of $125^2$.

  1. $13525$

  2. $15425$

  3. $15625$

  4. None of these


Correct Option: C

Identify the correct representation of the square of the number $205$ using Vedic Mathematics.

  1. $(20 \times 20)125$

  2. $(20 \times 25)5$

  3. $(20 \times 21)25$

  4. None of these


Correct Option: C
Explanation:

Next number of 20 is 21 .

20 × 21
So, square of 125 = (20 × 21)25

Find the square of $525$ using Vedic Mathematics.

  1. $234625$

  2. $2677525$

  3. $275985$

  4. $275625$


Correct Option: D
Explanation:

Next number of 52 is 53
square of 525 = (52 × 53) 25 = 275625

Find the square of $225$ using Vedic Mathematics.

  1. $125625$

  2. $125655$

  3. $105625$

  4. None of these


Correct Option: C
Explanation:

Next number of 22 is 23.
(22  ×23 ) = 506
Square of 225 = 50625

Find the square of the number $15$ using Vedic Mathematics.

  1. $125$

  2. $225$

  3. $625$

  4. None of these


Correct Option: B
Explanation:

Next number of 1 is 2.
Square of 15 = (1 × 2)25
= 225

Identify the correct representation in the square of $225$ using Vedic Mathematics.

  1. $(25\times2)625$

  2. $(125\times2)625$

  3. $(25\times25)125$

  4. None of these


Correct Option: A

Find the square of the number $205$ using Vedic Mathematics.

  1. $42025$

  2. $42125$

  3. $42325$

  4. None of these


Correct Option: A
Explanation:

Next number of 20 is 21 .

21 × 20 = 420
square of 5 = 25
So, square of 205 = 42025

Find the square of the number $125$ using Vedic Mathematics.

  1. $15625$

  2. $15525$

  3. $15325$

  4. None of these


Correct Option: A
Explanation:

Next number of 12 is 13 .

12 × 13 = 156
square of 5 = 25
So, square of 125 = 15625

Find the square of $925$ using Vedic Mathematics.

  1. $845625$

  2. $855225$

  3. $855625$

  4. None of these


Correct Option: C
Explanation:

Next number of 92 is 93
Square of 925 = (92 × 93)25 = 855625

Square of 659 by Sutra Ekadhikena Purvena is?

  1. 21456

  2. 434281

  3. 412356

  4. 52789


Correct Option: B
Explanation:

(659)2
= (659 + 1) (659 – 1) + 12
= 660 × 658 + 1
= 434280 + 1
= 434281

Identify the correct representation in the square of $925$ using Vedic Mathematics.

  1. $(95\times 95)\ | \ 125$

  2. $(95\times 9)\ |\ 625$

  3. $(95\times 96)\ | \ 125$

  4. None of these


Correct Option: B
Explanation:

Next number of 92 is 93
Square of 925 = (92 × 93)25 = 855625 = (95×9)|625

Square of 89 by Sutra Ekadhikena Purvena is?

  1. 4288

  2. 2166

  3. 7921

  4. 3356


Correct Option: C
Explanation:

(89)2
= (89 + 1) (89 – 1) + 12
= 90× 88 + 1
= 7920 + 1
= 7921

Square of 38 by  Upsutra Yavadunam Tavadunam Vargecha Yojayet is?

  1. 7854

  2. 1444

  3. 5634

  4. 8764


Correct Option: B

Find the square of the number $95$ using Vedic Mathematics.

  1. $9025$

  2. $9125$

  3. $8025$

  4. $8125$


Correct Option: A
Explanation:
To find $(95)^{2}$
$100$ is the nearest power of $10$ which can be taken out as base.
Deviation is obtained by $95-100=-5$
Left side of the number is $95-5=90$
Since, the base is $100$, the right hand side number will have two digits and that can be obtained by taking square of deviation $-5$. So, $(-5)^{2}=25$.
Thus, the right side number will be $25$.
Hence, the required number is $9025$.

Find the square of the number $105$ using Vedic Mathematics.

  1. $11125$

  2. $11235$

  3. $11325$

  4. $11025$


Correct Option: D
Explanation:
To find $(105)^{2}$
$100$ is the nearest power of $10$ which can be taken out as base.
Deviation is obtained by $105-100=5$
Left side of the number is $105+5=110$
Since, the base is $100$, the right hand side number will have two digits and that can be obtained by taking square of deviation $5$. So, $(5)^{2}=25$.
Thus, the right side number will be $25$.
Hence, the required number is $11025$.

Identify the correct representation of the square of the number $95$ using Vedic Mathematics.

  1. $(95 \times 10)5$

  2. $(9 \times 9)25$

  3. $(9 \times 10)125$

  4. $(9 \times 10)25$


Correct Option: D
Explanation:


$\underset { +5 }{ 95 }  \times \underset { +5 }{  95 } $                                                          Using base 10
                                                                       $9 = 9 \times  base$
Mutiply $5$ with $5 = 25$

Add $5$ to $95 = 100$

Multiply 9 to sum  $= 9\times 100 = 900$

 Take first 2 digits $= 90 = 9\times 10$
 
Last 2 digits $= 25$

$\therefore $   ${95 }^{ 2 } = (9\times 10)25$

When multiplied by itself, which number is equal to $12,345, 678, 987, 654, 321$?

  1. $1,111,111$

  2. $111,111,111$

  3. $11,111,111,111$

  4. $111,111,111,111$


Correct Option: B
Explanation:
$(1)^2=1$
$(11)^2=121$
$(111)^2=12321$
$(111, 111, 111)^2=12345678987654321$
Here we can show a pattern for each count of $1$ in $LHS$ is extended the number from $1$ to that Number and reverse that number to the $1$ in $RHS$

Square of $512$ by Ishta Sankhya method is?

  1. $262911$

  2. $365788$

  3. $262144$

  4. $356458$


Correct Option: C
Explanation:

Ishta number $=12$

Now finding the square
$=(512-12)(512+12)+{ (12) }^{ 2 }\ =500\times 524+144\ =262000+144\ =262144$
So option $C$ is correct.

Square of a $5$4 by Upsutra Yavadunam Tavadunam Vargecha Yojayet method is?

  1. $2686$

  2. $5656$

  3. $6966$

  4. $2916$


Correct Option: D
Explanation:

To find the square of $54$,


This is closer to $100$ (base of 10). Write it as $100-46$.

From this method, we can write,

$\dfrac{(54-46)}{46^2}$  i.e., $\dfrac{Number-deficiency}{deficiency^2}$

$=\dfrac{8}{2116}$

As we are using base $100$, digits in hundred's place and above is carry forwarded. Add $21$ to $8$.

ie., $(21+8)16=2916$

$2916$ is the square of $54$.

Square of 78 by Ishta Sankhya is?

  1. 6084

  2. 7084

  3. 2164

  4. 4524


Correct Option: A
Explanation:

Ishta number $=8$

Now finding the square
$=(78-8)(78+8)+8^2$
$=70\times 86+64$
$6020+64$
$=6084$
So option $A$ is correct.

What will be the value of $x$ if we have to find the square of number $93$ by Upsutra Yavadunam Tavadunam Vargecha Yojayet method
$93^2$=$(93-x)|(x^2)$=$8649$

  1. $3$

  2. $4$

  3. $7$

  4. $10$


Correct Option: C
Explanation:

$x=100-93=7$

$93^2=(93-7)|(7^2)=8649$

Say True or False
To find square of number by Sutra Ekadhikena Purvena method, the number should end with $5$.

  1. True

  2. False


Correct Option: A
Explanation:

We can find the square of the number which is ending with 5, using Ekadhikena purvena method.

To find the square of number by  Yavadunam Tavadunam Vargecha Yojayet method the number should be closer to the power of  $10$

  1. True

  2. False


Correct Option: A
Explanation:

The condition for using Yavadunam Tavadunam Vargecha Yojayet method- Numbers need to be close to the power of 10 (10, 100, 1000, etc).

State the following statement is True or False
We can find the square of number $43$ by Upsutra Yavadunam Tavadunam Vargecha Yojayet method

  1. True

  2. False


Correct Option: B
Explanation:

The condition for using Yavadunam Tavadunam Vargecha Yojayet method- Numbers need to be close to the power of 10 (10, 100, 1000, etc).

Square of $63$ by Sutra Urdhva-tiryagbhyam method is :

  1. $8529$

  2. $4569$

  3. $3969$

  4. $5479$


Correct Option: C
Explanation:

To find the square of $63$


$63 \ \times \ 63$

3 steps are there to solve this.

(i)  Multiply the unit digits
 $3 \times 3=9$

(ii) Take the units and tens digit to cross multiply and add the products
$(3\times6)+(6\times3)=18+18=36$

Keep $6$ intact and carry forward $3$ to next step.

(iii) Multiply the tens digits
$6\times6=36$

Add the carry forward $3$ to $36$.
$36+3=39$

Write the numbers obtained from step (iii) to (i) in order.
i.e., $3969$

This the square of $63$ is $3969$.

Square of $112$ by Sutra Urdhva-tiryagbhyam method is :

  1. $21844$

  2. $12544$

  3. $16544$

  4. $17644$


Correct Option: B
Explanation:

To find the square of $112$


$112 \ \times \ 112$

5 steps are there to solve this.

(i)  Multiply the unit digits
 $2 \times 2=4$

(ii) Take the units and tens digit to cross multiply and add the products
$(2\times1)+(1\times2)=2+2=4$

(iii) Take all three digits to cross multiply and add the products
$(2\times1)+(1\times2)+(1\times1)=2+2+1=5$

(iv) Take the hundreds and tens digit to cross multiply and add the products
$(1\times1)+(1\times1)=1+1=2$


(v) Multiply the hundred digits
$1\times1=1$


Write the numbers obtained from step (v) to (i) in order.
i.e., $12544$

This the square of $112$ is $12544$.

Square root of $20736.893$ Sub-sutra Anurupenya method is?

  1. $144.78$

  2. $144.11$

  3. $144.0031$

  4. $154.0021$


Correct Option: C

To find the square of $45$ by Ekadhikena Purvena method the digit $4$ should be multiplied by which number.

  1. By its previous number

  2. By zero

  3. By its next number

  4. By ten


Correct Option: C
Explanation:

In ekadhikena purvena the first digit is multiplied by its next number.

$45^2\Rightarrow $ First 2 digits $=4\times 5$
and last two digits are$=5^2=25\ \Rightarrow 45^2=2025$

Square of $113$ by Upsutra Yavadunam Tavadunam Vargecha Yojayet is :

  1. $34569$

  2. $12769$

  3. $54639$

  4. $34359$


Correct Option: B
Explanation:

To find the square of $113$,


This is closer to $100$ (base of 10). Write it as $100+13$.

From this method, we can write,

$\dfrac{(113+13)}{13^2}$  i.e., $\dfrac{Number+deficiency}{deficiency^2}$

$=\dfrac{126}{169}$

As we are using base $100$. Digit in hundred's place gets carryforwarded and added to $126$

ie., $(126+1)69=12769$

$12769$ is the square of $113$.

The Dvanda of 567 can be calculated as :- D(567)=$(x\times 5\times 7)$$+$$6^2$
What is the value of $x$?

  1. $2$

  2. $3$

  3. $4$

  4. $5$


Correct Option: A
Explanation:

$D(567)=(2\times 5\times 7)+6^2\ \therefore x=2$

Find the square of the number $65$ using Vedic Mathematics.

  1. $4235$

  2. $4335$

  3. $4220$

  4. None of these


Correct Option: D
Explanation:
To find $(65)^{2}$
Let's take $a=6$. So, $a5=10a+5$ 
Now, $a5$ square can be obtained as follows
$a5=a(a+1)|25$ where $a(a+1)$ is the left side of the number and right side will always be $25$ for the numbers ending with $5$.
Right side of $65$ will be $6\times 7=42$
and left side will be $25$.
So, the number is $4225$.
Hence, $65^{2}=4225$. 

Square root of $315$ by Dwandwa Yog method is?

  1. $17.84$

  2. $17.74$

  3. $17.54$

  4. $17.64$


Correct Option: B

State the following statement is true or false
We can find the squares of all the numbers using dwandwa yog method

  1. True

  2. False


Correct Option: A
Explanation:

The Vedic method of finding a square root is called the Vedic Duplex method also known as dvandva yog method. As the name implies, the method involves a concept called the duplex of a number.



Square root of $732108$ by Dwandwa Yog method is?

  1. $256.63$

  2. $896.25$

  3. $745.23$

  4. $855.63$


Correct Option: D

Predict square root of $3136$ using Vilokanam method.

  1. $54$

  2. $56$

  3. $64$

  4. $66$


Correct Option: B
Explanation:

We have to find the square root of $3136$ using Vilokanam method.

Its unit digit is $6$.
Therefore, the unit digit of the square root will be $4$ or $6$. 
Ignoring the last two digits (unit digit and ten’s digit) we get $31$. 
The greatest number whose square is less than or equal to $31$ is $5$.
Adjusting above obtained two unit digits $4$ or $6$ to the right of $5$, we get two numbers $54$ and $56$. 
The unique number with unit digit $5$ which lies between $54$ and $56$ is $55$. 
And  $(55)^2 = 3025$
Since, $3136>3025$, therefore, the required square root is $56$.
Thus $\sqrt{3136}=56$

Find square root of $9604$ using Vilokanam method.

  1. $98$

  2. $92$

  3. $88$

  4. $82$


Correct Option: A
Explanation:

We have to find the square root of $9604$ using Vilokanam method.

Its unit digit is $4$.
Therefore, the unit digit of the square root will be $2$ or $8$. 
Ignoring the last two digits (unit digit and ten’s digit) we get $96$. 
The greatest number whose square is less than or equal to $96$ is $9$.
Adjusting above obtained two unit digits $2$ or $8$ to the right of $9$, we get two numbers $92$ and $98$. 
The unique number with unit digit $5$ which lies between $92$ and $98$ is $95$. 
And  $(95)^2 = 9025$
Since, $9604>9025$, therefore, the required square root is $98$.
Thus $\sqrt{9604}=98$

Find square root of $961$ using Vilokanam method.

  1. $29$

  2. $30$

  3. $31$

  4. $32$


Correct Option: C
Explanation:

We have to find the square root of $961$ using Vilokanam method.

Its unit digit is $1$.
Therefore, the unit digit of the square root will be $1$ or $9$. 
Ignoring the last two digits (unit digit and ten’s digit) we get $9$. 
The greatest number whose square is less than or equal to $9$ is $3$.
Adjusting above obtained two unit digits $1$ or $9$ to the right of $2$, we get two numbers $31$ and $39$. 
The unique number with unit digit $5$ which lies between $31$ and $39$ is $35$. 
And  $(35)^2 = 1225$
Since, $961<1225$, therefore, the required square root is $31$.
Thus $\sqrt{961}=31$

Using vedic mathematics term "Ekadhik", find the value of $105^2$.

  1. $11025$

  2. $12025$

  3. $11245$

  4. $12235$


Correct Option: A

Using vedic mathematics term "Ekadhik", find the value of $165^2$.

  1. $27425$

  2. $27225$

  3. $24625$

  4. None of these


Correct Option: B

Find square root of $78676$ using Dwandwa Yog method.

  1. $280.24$

  2. $280.34$

  3. $280.49$

  4. $280.63$


Correct Option: C

Find square root $5958$ using first principle method(Vargamula method).

  1. $77.173$

  2. $77.188$

  3. $77.167$

  4. $77.159$


Correct Option: B

Find square root $1089$ using first principle method(Vargamula method).

  1. $19$

  2. $23$

  3. $29$

  4. $33$


Correct Option: D

Find square root $2025$ using first principle method(Vargamula method).

  1. $41$

  2. $43$

  3. $45$

  4. $47$


Correct Option: C

Find square root of $98327$ using Dwandwa Yog method.

  1. $313.67$

  2. $313.45$

  3. $313.34$

  4. $313.57$


Correct Option: A

Find square root $155.56$ using first principle method(Vargamula method).

  1. $12.47$

  2. $12.43$

  3. $12.39$

  4. $12.35$


Correct Option: A

Square root of $17689$ by Dwandwa Yog method is

  1. $783$

  2. $133$

  3. $233$

  4. $653$


Correct Option: B
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