Existence of irrational numbers - class-XI
Description: existence of irrational numbers | |
Number of Questions: 109 | |
Created by: Blackmamba | |
Tags: real numbers maths number systems real numbers (rational and irrational numbers) basic algebra rational and irrational numbers |
$A,B,C$ and $D$ are all different digits between $0$ and $9$. If $AB+DC=7B\ (AB,DC$ and $7B$ are two digit numbers), then the value of $C$ is
If $\sqrt{a}$ is an irrational number, what is a?
Which of the following is irrational
The number $23+\sqrt{7}$ is
Which of the following rational number represents a terminating decimal expansion?
Say true or false:
Read out each of the following numbers carefully and specify the natural numbers in it.
$87, 54, 0, -13, -4.7, \sqrt{7}, 2{1}{7}, \sqrt{15}, -{8}{7}, 3\sqrt{7}, 4.807, 0.002, \sqrt{16}$ and $2+\sqrt{3}.$
There can be a pair of irrational numbers whose sum is irrational
State true or false:
Simplify :
Which of the following is irrational?
$\sqrt 7$ is
State whether the following statement are true or false? Justify your answers.
State whether the following statement are true or false? Justify your answers.
Classify the following numbers as rational or irrational : $2-\sqrt{5}$
Decimal representation of an irrational number is always
Are the square roots of all positive integers irrational?
Which among the following is true?
The decimal expansion of the number $\sqrt{2}$ is
State True or False.
State True or False.
State True or False.
State True or False.
State True or False.
State True or False.
State True or False.
State True or False.
State True or False.
State TRUE or FALSE
Value of $\pi$ is equal to (approximately)
$\sqrt3$ is
$\sqrt2 + \sqrt3$ is
Every surd is
Which of the following is irrational?
$0.\overline{35}$ is equal to
$3.\overline{25}$ is equal to
$0.\overline{05}$ is equal to
Which statement is true?
Irrational number is defined as
The square root of any prime number is
$\dfrac {7}{9}$ is a/an _______ number.
$\sqrt {23}$ is not a ...... number.
$(3 + \sqrt {5})$ is ..............
$m$ is not a perfect square, then $\sqrt {m}$ is
$\pi = 3.14159265358979........$ is an
How many of the following four numbers are rational?
$\sqrt{3}+\sqrt{3}, \sqrt{3}-\sqrt{3}, \sqrt{3} \times \sqrt{3}, \sqrt{3} / \sqrt{3}$
Which of the following are irrational numbers?
Consider the following statements:
1. $\dfrac {1}{22}$ cannot be written as a terminating decimal.
2. $\dfrac {2}{15}$ can be written as a terminating decimal.
3. $\dfrac {1}{16}$ can be written as a terminating decimal.
Which of the statements given above is/are correct?
State whether the following statements are true or false. Justify your answers.
Every real number need not be a rational number
State whether the following statement is true or false:
All real numbers are irrational
Classify the following numbers as rational or irrational: $\displaystyle \frac{\sqrt{12}}{\sqrt{75}}$
Which of the following number is different from others?
Which of the following are irrational numbers?
(i) $\sqrt{2+\sqrt{3}}$
(ii) $\sqrt{4+\sqrt{25}}$
(iii) $\sqrt[3]{5+\sqrt{7}}$
(iv) $\sqrt{8-\sqrt[3]{8}}$.
Which one of the following is an irrational number?
Let $x$ be an irrational number then what can be said about ${x}^{2}$
State the following statement is true or false.
The product of a non-zero rational number with an irrational number is always :
Which is not an Irrational number?
$\left ( 2+\sqrt{5} \right )\left ( 2+\sqrt{5} \right )$ expression is :
A pair of irrational numbers whose product is a rational number is:
A number is an irrational if and only if its decimal representation is :
Which of the following is not an irrational number?
$\pi$ is _______
Which of the following number is irrational ?
Which one of the following is an irrational number ?
A number is an irrational if and only if its decimal representation is :
Which of the following is an irrational number ?
$\pi$ is a(n) ________ while $\dfrac{22}{7}$ is rational.
$\sqrt{5}$ is an irrational number.
$\dfrac{1}{\sqrt{2}}$ is an irrational number.
$3+2\sqrt{5}$ a rational number.
$\sqrt { 2 } ,\sqrt { 3 }$ are
If $p$ is prime, then $\sqrt{p}$ is irrational and if $a, b$ are two odd prime numbers, then $a^2 -b^2$ is composite. As per the above passage mark the correct answer to the following question.
$\sqrt{7}$ is:
Consider the given statements:
I. All surds are irrational numbers.
II. All irrationals numbers are surds.
Which of the following is true.
Which of the following numbers is different from others?
If $a\neq 1$ and $ln{ a }^{ 2 }+{ \left( ln{ a }^{ 2 } \right) }^{ 2 }+{ \left( ln{ a }^{ 2 } \right) }^{ 3 }+........=3\left( lna+{ \left( ln{ a } \right) }^{ 2 }+{ \left( ln{ a } \right) }^{ 3 }+{ \left( ln{ a } \right) }^{ 4 }+...... \right)$ then $a$ is
Simplify the following expressions.
Classify the following numbers as rational or irrational.
Which of the following numbers are an irrational number.
If $p$ and $q$ are two distinct irrational numbers, then which of the following is always is an irrational number
$\sqrt 7 $ is irrational.
Say true or false:$0.120 1200 12000 120000 $....is a rational number
State True or False.
The number $\displaystyle\frac{3-\sqrt{3}}{3+\sqrt{3}}$ is
Give an example of two irrational numbers, whose sum is a rational number
Give an example of two irrational numbers, whose difference is an irrational number.
Give an example of two irrational numbers, whose quotient is an irrational number.
Give an example of two irrational numbers, whose sum is an irrational number.
Give an example of two irrational numbers, whose quotient is a rational number.
Give an example of two irrational numbers, whose product is a rational number.
Give an example of two irrational numbers, whose product is an irrational number.
$\displaystyle log _{4}18$ is
Number of integers lying between $1 $ to $102$ which are divisible by all $\displaystyle \sqrt{2},\sqrt{3},\sqrt{6}, $ is
Simplify by combining similar terms :$\displaystyle 3\sqrt{147}-\frac{7}{3}\sqrt{\frac{1}{3}}+7\sqrt{\frac{1}{3}}$
Which of the following is an irrational number?
$\sqrt {5}$ is a\an ......... number.
How many irrational numbers are there between $2$ and $6$?
$\sqrt{21-4\sqrt{5}+8\sqrt{3}-4\sqrt{15}}=$...........
State whether the following statements are true or false.
$\sqrt {n}$ is not irrational if n is a perfect square
If $p$ is prime, then $\sqrt {p}$ is:
State the following statement is true or false
$6+\sqrt{2}$ is a rational number.