Irrational Numbers

Q.

Prove that$\sqrt{2}$ is an irrational number.

Q.

Prove that the following is irrational : $\frac{1}{\sqrt{2}}$

Q.

Prove that $(4-5\sqrt{2})$ is an irrational number.

Q. Express the number 0.3178(bar on 178) in the form of rational number p/q

Q.

Show that root 3 +root 5 is an irrational number

Q. Show that √p+√q is an irrational number where p and q are prime numbers.

Q.

Prove 7/3√2 an irrational??

Q. Question 7
Which of the following is irrational?

A) 0.14
B) $0.14\overline{16}$
C) $0.\overline{1416}$
D) 0.4014001400014

Q.

Question 8
The product of a non – zero rational and an irrational number is

A) Always irrational
B) Always rational
C) Rational or irrational
D) One

Q.

Show that $3\sqrt{2}$ is irrational.

Q.

If p is a prime number , then prove that √p is irrational.

Q.

Prove that $3+\surd 5$ is irrational

Q.

The numbers which have a non-terminating and non-repeating decimal expansion or cannot be represented in the form of $\frac{p}{q}$ (q is not equal to '0') are known asnumbers.

Q.

A circle has a radius of 5 cm. What is the nature of its perimeter?

1. Irrational

2. Rational

3. can't say

4. Integer

Q.

If p, q are prime positive integers, prove that √p+ √q is an irrational number.

My doubt: how to find whether √p is an irrational number???

Q.

Prove that for any prime positive integer p , √p is an irrational number.

Q. $3.\overline{27}$ is

(a) an integer
(b) a rational number
(c) a natural number
(d) an irrational number

Q. Has the rational number $\frac{441}{2^2\times 5^7\times 7^2}$a terminating or a nonterminating decimal representation?

Q.

Prove that root 2 + root 5 is an irrational number

Q.

Prove that root 3 is an irrational number .Hence prove that 3(2 root 3) is an irrational number.

Q.

Prove that √2. is an irrational number by contradiction method

Q.

Prove that 1+1/√2 is irrational

Q.

Which of the following is an irrational number?

1. 14.287628762876.....

2. 15.2323232323......

3. 5.2731687143725186.....

4. 1.33333333...

Q. If irrational number cannot be expressed in the form p/q where p and q are integers, and q is not = 0, then why pi is irrational though it is represented in the form p/q

Q.

Which of the following is always rational?

1. The hypotenuse of a right angled triangle having rational base and perpendicular
2. The area of a triangle​, given the value of the sides are irrational
3. The area of rectangle in which the value of one of the sides is irrational
4. The volume of a cube, given the value of the sides are rational

Q.

If root6 is irrational then prove 5root6 is rational

Q.

Classify the following numbers as rational or irrational:

$\left(i\right)\frac{22}{7}\left(ii\right)3.1416\left(iii\right)\pi \left(iv\right)3.\overline{142857}\left(v\right)\mathrm{5.636363...}\left(vi\right)\mathrm{2.040040004...}\left(viii\right)\mathrm{1.535335333....}\left(viii\right)\mathrm{3.121221222...}\left(ix\right)\sqrt{21}\left(x\right)\sqrt[3]{33}$

Q. Prove that for any prime positive integer p, $\sqrt{p}$ is an irrational number.

Q.

What is the difference between real numbers and rational numbers ?

Q.

Prove that the sum of a rational number and an irrational number is always irrational.