Rationalisation

Q. Find the square root of $7-4\sqrt{3}$

1. $2+\sqrt{3}$
2. $5-\sqrt{3}$
3. $2-\sqrt{3}$
4. $5+\sqrt{3}$

Q. If $\frac{3+\sqrt{5}}{2\sqrt{5}+3}=a+b\sqrt{5}$, then the values of irrational numbers a and b are

1. $\frac{1}{11},\frac{3}{11}$
2. $7,\frac{8}{11}$
3. $5,11$
4. $\frac{2}{11},\frac{3}{11}$

Q. What is the value of $2\sqrt[3]{33}\times 3\sqrt[3]{34}\times 4\sqrt[3]{35}$

1. $60\times \sqrt[3]{324}$
2. $40\times \sqrt[3]{324}$
3. $24\times \sqrt[3]{360}$
4. $60\times \sqrt[3]{360}$

Q. Simplify by rationalising the denominator:
$\frac{7\sqrt{3}-5\sqrt{2}}{\sqrt{48}+\sqrt{18}}$

1. $\frac{114-41\sqrt{6}}{30}$
2. $\frac{114+41\sqrt{6}}{30}$
3. $-\frac{114-41\sqrt{6}}{30}$
4. $-\frac{114+41\sqrt{6}}{30}$

Q. Simplified form after rationalising the denominator: $\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2\sqrt{5}}{\sqrt{6}+\sqrt{5}}$ is $-\sqrt{m}+7$. Find $m$.

Q. The sum of two nonzero real numbers is $6.$ Then the minimum value of the sum of their reciprocals is ?

Q. $5-2\sqrt{6}$

1. $\sqrt{13}-\sqrt{2}$
2. $\sqrt{5}-\sqrt{3}$
3. $\sqrt{3}-\sqrt{2}$
4. $\sqrt{5}-\sqrt{2}$

Q.

1. $9+2\sqrt{15}$
2. $9-2\sqrt{15}$
3. $9+2\sqrt{9}$
4. $9-2\sqrt{9}$

Q.

If $p=3-2\sqrt{2}$, then $p^2+\frac{1}{p^2}=$ ______.

1. 34

2. 35

3. 36

4. 38

Q. Find the sum up to 91 terms of the following
$\frac{1}{\sqrt{9}+\sqrt{10}}+\frac{1}{\sqrt{10}+\sqrt{11}}+\frac{1}{\sqrt{11}+\sqrt{12}}+.....$

1. $90$
2. $10$
3. $7$
4. $1$