Division of Surds by Rationalisation

Q.

If $x=6-\sqrt{35}$, then $x^2+\frac{1}{x^2}=$ ___

1. 140

2. 120

3. 144

4. 142

Q.

$\frac{4}{1-\sqrt{2}-\sqrt{3}}=$ ____________.

1. $2-\sqrt{2}-\sqrt{6}$

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

3. 4

4. $2-\sqrt{2}+\sqrt{6}$

Q.

How do you simplify ${\left(\frac{1}{2}\right)}^{-2}$?

Q. The value of $\frac{(0.6{)}^0-(0.1{)}^{-1}}{\left(\frac{3}{2^3}{)}^{-1}\right(\frac{3}{2}{)}^3+(-\frac{1}{3}{)}^{-1}}$ is _____________.

1. $\frac{-1}{2}$
2. $\frac{2}{3}$
3. $\frac{3}{2}$
4. $\frac{-3}{2}$

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

1. 2

Q. $\text{If}m=\frac{1}{5+\sqrt{26}}\text{then,}{m}^2=$ _______.

Q.

If 'a' and 'b' are rational numbers, then find the values of 'a' and 'b' given that $\frac{2+5\sqrt{3}}{2-\sqrt{3}}=a+b\sqrt{3}$

1. a = 19 , b = 12

2. a = 12 , b = 19

3. a = 20 , b = 13

4. a = 9 , b = 2

Q.

Simplify the following using the identities : ${(\frac{x}{4}+\frac{5}{y})}^2$

Q. If $x=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$ and $y=\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$, then find $x+y+xy$
$\left[4\right]$

Q.

If a and b are rational numbers, find 'a' and 'b' when

$\frac{\sqrt{7}-2}{\sqrt{7}+2}=a\sqrt{7}+b$

1. $a=-\frac{4}{3},b=\frac{-11}{3}$

2. $a=\frac{4}{3},b=\frac{-11}{3}$

3. $a=\frac{4}{3},b=\frac{11}{3}$

4. $a=\frac{-4}{3},b=\frac{11}{3}$

Q. When expanded, the number of zeroes in ${1000}^{10}$ is ______.

1. 30
2. 10
3. 13
4. 4

Q. Match the following to their simplified values.

1. 4
2. $2+\sqrt{3}$
3. 11 + 6$\sqrt{2}$