Rationalising Factor

Q.

Simplify $\frac{1}{2-\sqrt{7}}$ by rationalising the denominator.

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

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

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

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

Q.

Rationalise the denominator in $\frac{5}{3\sqrt{3}}$

1. $\frac{5\sqrt{5}}{9}$

2. $\frac{5\sqrt{1}}{9}$

3. $\frac{5\sqrt{3}}{3}$

4. $\frac{5\sqrt{3}}{9}$

Q.

Rationalise the denominator in $\frac{2}{\sqrt{3}}$ .

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

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

3. $\frac{2\sqrt{3}}{3}$

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

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.

Rationalise the denominator of $\frac{2+\sqrt{5}}{2-\sqrt{5}}$

1. $-(9-2\sqrt{5})$

2. $-(9+4\sqrt{5})$

3. $9-4\sqrt{5}$

4. $4-9\sqrt{5}$

Q.

Rationalising factor of $\frac{1}{\sqrt{3}+\sqrt{5}}$ is

1. 

2. 

3. 

4. 

Q.

What is the least rationalising factor of $\sqrt{44}$?

1. $\sqrt{5}$

2. $\sqrt{2}$

3. $\sqrt{43}$

4. $\sqrt{11}$

Q.

What is the least rationalising factor of $\sqrt{72}$?

1. $\sqrt{3}$

2. $\sqrt{5}$

3. $\sqrt{7}$

4. $\sqrt{2}$

Q.

Simplify $\frac{3}{\sqrt{5}+\sqrt{3}}$ by rationalising the denominator.

1. $\frac{3(\sqrt{3}-\sqrt{5})}{2}$

2. $\frac{3(\sqrt{5}-\sqrt{3})}{2}$

3. $\frac{3(\sqrt{5}-\sqrt{3})}{8}$

4. $\frac{3(\sqrt{5}-\sqrt{2})}{2}$

Q.

$\frac{4+\sqrt{5}}{4-\sqrt{5}}+\frac{4-\sqrt{5}}{4+\sqrt{5}}=$ ___

1. $2$

2. $1$

3. $\frac{21}{11}$

4. $\frac{42}{11}$