Multiplication and Division of Surds

Q.

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

1. 34

2. 35

3. 36

4. 38

Q. $\sqrt{2}$ is not an irrational number.

1. True
2. False

Q. State true or false $\frac{\sqrt{2}}{\sqrt{3}}$ gives an irrational value

1. False
2. True

Q.

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

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. State true or false.
$\frac{\sqrt{2}}{\sqrt{3}}$ gives an irrational value.

1. True
2. False

Q. Examine, whether the following numbers are rational or irrational:
$\frac{10}{2\sqrt{5}}$

Q.

$(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})=$_____.

1. 3

2. 1

3. 6

4. 4

Q.

Find the value of $\sqrt[5]{516}\times \sqrt[5]{52}$.

1. 32

2. 4

3. $\sqrt[5]{518}$

4. 2

Q.

If $\frac{5}{\sqrt{3}-\sqrt{2}}=a\sqrt{3}-b\sqrt{2}$, then the values of 'a' and 'b' are _________.

1. $a=5,b=5$

2. $a=-5,b=-5$

3. $a=-5,b=5$

4. $a=5,b=-5$

Q.

If $\frac{\sqrt{3}-1}{\sqrt{3}+1}=a+b\sqrt{3}$, then the values of ${}^{\prime }{a}^{\prime }$ and ${}^{\prime }{b}^{\prime }$ are _________.

1. $a=2,b=-1$

2. $a=-2,b=1$

3. $a=4,b=-1$

4. $a=2,b=1$

Q.

Simplify: $(3\sqrt{3}+2\sqrt{2})$$(2\sqrt{3}+3\sqrt{2})$

1. $30+13\sqrt{6}$

2. $24+6\sqrt{6}$

3. $30+6\sqrt{6}$

4. $24+13\sqrt{6}$

Q. $\sqrt{10}\times \sqrt{15}=$ ______

1. $6\sqrt{5}$
2. $5\sqrt{6}$
3. $25$
4. $10\sqrt{5}$

Q.

What is the value of $\frac{16\sqrt{13}}{9\sqrt{52}}$ ?

1. $\frac{3}{9}$

2. $\frac{9}{8}$

3. $\frac{7}{9}$

4. $\frac{8}{9}$

Q. Simplify the following expression :

iii) $(\sqrt{8}-\sqrt{2})(\sqrt{8}+\sqrt{2})$

Q.

Fill in the blanks:

$\frac{6}{15}=\frac{1}{\square }=\frac{18}{\square }$

Q.

The value of $\frac{\left\{{\left(\sqrt{\sqrt{3}+1}+\sqrt{\sqrt{3}-1}\right)}^2\left(\sqrt{3}-\sqrt{2}\right)\right\}}{{\left(\sqrt{\sqrt{3}+1}\right)}^2-{\left(\sqrt{\sqrt{3}-1}\right)}^2}$ is

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

2. $1$

3. $\sqrt{3}$

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

Q. State true or false $\frac{\sqrt{2}}{\sqrt{3}}$ gives an irrational value

1. True
2. False

Q.

$2\sqrt{3}\times 3\sqrt{2}$ is ___. (rational/irrational)

.

Q. $(1+\sqrt{2})(2+\sqrt{3})=$

1. 2+3+22+6
2. 2+23+22+6
3. 2+3+2+6

Q. Find the value of p and q if $\frac{\sqrt{13}+\sqrt{5}}{\sqrt{13}-\sqrt{5}}=p-q\sqrt{65}$.