Sqrt(P) Is Irrational, When 'P' Is a Prime

Q.

Prove that $\frac{2}{\sqrt{7}}$ is irrational.

Q. Given that $\sqrt{2}$ is irrational, prove that $(5+3\sqrt{2})$ is an irrational number.

Q.

Prove that $2+\sqrt{3}$ is an irrational number.

Q.

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

Q.

Prove that $5\sqrt{2}$ is irrational.

Q.

Let $X$ and $Y$ be the sets of all positive divisors of $400$ and $1000$ respectively (including $1$ and the number). Then $n(X\cap Y)=$

1. $4$

2. $6$

3. $8$

4. $12$

Q. $1+\sqrt{3}$ is a real rational number.

1. True
2. False

Q.

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

Q. Prove that $\sqrt{p}+\sqrt{q}$ is irrational, where p and q are primes.

Q.

Prove root $5$ is an irrational number.

Q. Prove that $(2\sqrt{3}-1)$ is an irrational number.

Q.

Question 14
Prove that $\sqrt{p}+\sqrt{q}$ is irrational, where p and q are primes.

Q. Prove that $\sqrt{p}+\sqrt{q}$ is irrational, where p and q are primes.

Q. Which of the following is/are an irrational number?

1. $\pi$
   
2. $\sqrt{5}$
   
3. $\sqrt{7}$
4. $\frac{22}{7}$

Q.

Prove that each of the following numbers is irrational.

$\left(i\right)\sqrt{3}\left(ii\right)(2-\sqrt{3})\left(iii\right)(3+\sqrt{2})\left(iv\right)(2+\sqrt{5})\left(v\right)(5+3\sqrt{2})\left(vi\right)3\sqrt{7}\left(vii\right)\frac{3}{\sqrt{5}}\left(viii\right)(2-3\sqrt{5})\left(ix\right)(\sqrt{3}+\sqrt{5})$

Q. Prove that $\frac{1}{\sqrt{2}}$ is irrational.

Q.

Prove that $\frac{2}{\sqrt{7}}$ is irrational.

Q. $\sqrt{3}$ is proved irrational by _____.

1. factorisation
2. rationalisation
3. contradiction
4. expansion

Q.

Prove that $\sqrt{2}+\sqrt{3}$ is irrational. [3 MARKS]

Q. State true or false.
$\sqrt{2}$ and $\sqrt{3}$ are irrational numbers.

1. True
2. False

Q. Below are the steps with respect to proving $\sqrt{2}$ as an irrational number. Choose the correct order of the steps.

1. Arrive at the contradiction as a and b were assumed to be co-prime.
2. Assume$\sqrt{2}$ to be rational, that is, $\sqrt{2}=\frac{a}{b},(b\ne 0)$ such that $a$ and $b$ are co-primes.
3. Carry forward a few computations to get 2 as a common factor of a and b.

1. 1, 2, 3
2. 2, 1, 3
3. 2, 3, 1
4. 3, 2, 1

Q.

Prove that the following is irrational : $7\sqrt{5}$ [2 MARKS]

Q.

Question 2
Prove that $3+2\sqrt{5}$ is irrational.

Q. Prove that $6+\sqrt{2}$ is irrational.

Q.

Prove that the following is irrational : $6+\sqrt{2}$ [3 MARKS]

Q.

Rationalize the denominator of :
$\frac{1}{(\sqrt{7}-\sqrt{6})}$ .

Q. $\sqrt{3}$ is proved irrational by _____.

1. factorisation
2. rationalisation
3. contradiction
4. expansion

Q.

Prove that $\sqrt{5}$ is irrational.

Q. Which of the following is/are rational number(s) ?

1. $\sqrt{2}$
2. $\frac{5}{2}$
3. $\frac{3}{2}$
4. $\sqrt{4}$

Q.

When we divide two surds, we may or may not get a rational number.

1. True

2. False