Simplest Form of a Surd

Q.

Simplify the following expression $\left(3+\sqrt{3}\right)\left(2+\sqrt{2}\right)$

Q. Simplify $\frac{6}{2\sqrt{3}-\sqrt{6}}+\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}-\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}}$

1. 1
2. 3
3. 0
4. 2

Q. The value of $\frac{4+\sqrt{5}}{4-\sqrt{5}}+\frac{4-\sqrt{5}}{4+\sqrt{5}}$ is:

1. 
2. 
3. 
4. 

Q.

Simplify the sum or difference: $\sqrt{5}+6\sqrt{5}$.

1. $6\sqrt{5}$

2. $30$

3. $6\sqrt{10}$

4. $7\sqrt{5}$

Q.

If $x=\frac{1}{\sqrt{3}+1}$ then the value of $x+\frac{1}{x}$ is

1. 

2. 

3. 

4. 

Q. $\text{Simplify}\sqrt{\frac{12}{121}}$

1. $\frac{2\sqrt{3}}{11}$
2. $\frac{3\sqrt{2}}{11}$
3. $\frac{5\sqrt{2}}{11}$
4. None of these

Q.

Simplify the sum or difference: $3\sqrt{7}-\sqrt{63}$

1. $-2\sqrt{7}$

2. $-6\sqrt{7}$

3. $-4\sqrt{3}$

4. $0$

Q.

Simplify the product: $\sqrt{6}(\sqrt{2}+\sqrt{3})$.

1. $\sqrt{8}+3$

2. $\sqrt{30}$

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

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

Q.

Simplify the sum or difference: $-6\sqrt{10}+5\sqrt{90}$

1. $9\sqrt{10}$

2. $-9\sqrt{10}$

3. $-39\sqrt{10}$

4. $-10$

Q. If $x=3+2\sqrt{2}$, then find the value of $(\sqrt{x}-\frac{1}{\sqrt{x}}).$

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

Q.

Simplify the sum or difference : $4\sqrt{2}-7\sqrt{2}$

1. $-\sqrt{6}$

2. $-3\sqrt{2}$

3. $-11\sqrt{2}$

4. $11\sqrt{2}$

Q.

The value of $3\sqrt{54}÷2\sqrt{2}$ is

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

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

3. $\frac{9\sqrt{3}}{2}$

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

Q. Find the value of $a+b+c$, if $\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}=a-b\sqrt{c}$

1. 20

Q. $\text{Simplify}\sqrt{\frac{12}{121}}$

1. $\frac{2\sqrt{3}}{11}$
2. $\frac{3\sqrt{2}}{11}$
3. $\frac{5\sqrt{2}}{11}$
4. None of these

Q. Find the value of $a+b+c$, if $\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}=a-b\sqrt{c}$

1. 20