Rationalisation of Surds

Q.

If 'p' and 'q' are rational numbers, then find the values of 'p' and 'q' given that $\frac{4-2\sqrt{3}}{2+\sqrt{3}}=p\sqrt{6}+q$

1. $p=4\sqrt{3},q=14$

2. $p=-4\sqrt{2},q=14$

3. $p=-4\sqrt{3},q=-14$

4. $p=4\sqrt{2},q=14$

Q.

The rationalising factor for the number $3-7\sqrt{2}$ is

1. $3+2\sqrt{7}$

2. $-3-2\sqrt{7}$

3. $3+7\sqrt{2}$

4. $-3+7\sqrt{2}$

Q.

The least rationalising factor of 5$\sqrt{x}$ is ______.

1. $5\sqrt{x}$

2. $5$

3. $x$

4. $\sqrt{x}$

Q.

Find the value of $\frac{1}{3-\sqrt{8}}-\frac{1}{\sqrt{8}-\sqrt{7}}+\frac{1}{\sqrt{7}-\sqrt{6}}-\frac{1}{\sqrt{6}-\sqrt{5}}+\frac{1}{\sqrt{5}-2}$ .

1. 1

2. 6

3. 4

4. 5