Rationalization of an Irrational Number

Q. Value of $(3+\sqrt{5})(3-\sqrt{5})$ is .

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

Q. Sort the given expressions in decreasing order.
(Highest on top)
Given:
$a=\frac{1}{3},b=-\frac{1}{3}$

1. ${125}^b$
2. ${64}^a$
3. $(125+64{)}^{a+b}$
4. ${64}^b+{125}^a$

Q. $\text{If}{\left(\sqrt{4096}\right)}^3=8^x\text{, then}x\text{is}$ ________.

1. 6
2. 4
3. 2
4. 5

Q.

Write any three different forms of the formula $(a+b{)}^2$.

Q.

Evaluate using the identities : ${\left(99\right)}^2-{\left(98\right)}^2$

Q.

The rationalising factor for the number $3-7\sqrt{2}$ is

1. $3+2\sqrt{7}$

2. $-3-2\sqrt{7}$

3. $3+7\sqrt{2}$

4. $-3+7\sqrt{2}$

Q. If $2^a=3^b=6^c$, then $c=$ .

1. $\frac{ab}{a+b}$
2. $\frac{a}{a+b}$
3. $\frac{a}{1+b}$
4. $\frac{abc}{a+b}$

Q. If $(4+\sqrt{13})\times (5-\sqrt{13})\times (7-\sqrt{13})=$ $6x$, then find $x$.

1. 6

Q.

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

1. $1$

2. $5$

3. $-1$

4. $0$

Q.

Find the value of $(3+\sqrt{5})(3-\sqrt{5})$ .

1. 1

2. 3
3. 4
4. 2

Q. Match the following:

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

Q.

Rationalising $\frac{\sqrt{2}+\sqrt{3}}{\sqrt{3}-\sqrt{2}}$ will give __________.

1. $5-2\sqrt{6}$

2. $5+2\sqrt{6}$

3. $7+2\sqrt{6}$

4. $7-2\sqrt{6}$

Q. $(\sqrt{4}+\sqrt{3})\times (\sqrt{4}-\sqrt{3})=$

1. 1
2. 2
3. 7
4. 3

Q.

Evaluate using the identities : ${\left(83\right)}^2-{\left(18\right)}^2$

Q. ${64}^{-\frac{1}{3}}[{64}^{\frac{1}{3}}-{64}^{\frac{2}{3}}]=$ .

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