Monomial and Binomial Surds

Q. Question 4
If $a=\frac{3+\sqrt{5}}{2}$, then find the value of $a^2+\frac{1}{a^2}$.

Q.

$\frac{\sqrt{6}-\sqrt{5}}{\sqrt{6}+\sqrt{5}}$ = ________.

1. $4\sqrt{30}$

2. $11-2\sqrt{30}$

3. $11-\sqrt{30}$

4. 11

Q.

Question 2 (i)
Simplify $(3+\sqrt{3})(2+\sqrt{2})$ .

Q.

The expression $\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$ when simplified reduces to $a-b\sqrt{15}$.

Find the value of a + b .

Q. Question 2
Simplify:
$\frac{7\sqrt{3}}{\sqrt{10}+\sqrt{3}}-\frac{2\sqrt{5}}{\sqrt{6}+\sqrt{5}}-\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}$

Q. Simplify the following :
(i)$4\sqrt{28}÷3\sqrt{7}÷\sqrt[3]{37}\left(ii\right)3\sqrt{3}+2\sqrt{27}+\frac{7}{\sqrt{3}}$

Q.

Rationalize the denominator of $\frac{1}{\sqrt{2}}$.

1. √2/2

2. 4/√2

3. 2/√2

4. √2/4

Q. Simplify : $\frac{\sqrt{3}}{\sqrt{2}}+\frac{\sqrt{2}}{\sqrt{3}}$

1. $\frac{6}{\left(\sqrt{5}\right)}$
2. $\frac{2}{\left(\sqrt{5}\right)}$
3. $\frac{5}{\left(\sqrt{6}\right)}$
4. $\frac{5}{\left(\sqrt{2}\right)}$

Q. The value of $(5-\sqrt{13})(5+\sqrt{13})$ is :

1. 12
2. 13
3. 25
4. 10

Q. Simplify the following :
(i)$4\sqrt{28}÷3\sqrt{7}÷\sqrt[3]{37}\left(ii\right)3\sqrt{3}+2\sqrt{27}+\frac{7}{\sqrt{3}}$

Q. Simplify the following :
(i)$4\sqrt{28}÷3\sqrt{7}÷\sqrt[3]{37}\left(ii\right)3\sqrt{3}+2\sqrt{27}+\frac{7}{\sqrt{3}}$