Rationalisation

Q. Simplify the following expressions:
$(3+\sqrt{3})(2+\sqrt{2})$
[2 Marks]
[NCERT]
[Operations on Real Numbers]

Q.

Find the values of $a$ and $b$

if $\frac{5+2\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3}$

1. $a=11,b=-6$

2. $a=9,b=-6$

3. $a=-11,b=6$

4. $a=-9,b=6$

Q.

Simplify $\left(\frac{2+\sqrt{5}}{2-\sqrt{5}}\right)+\left(\frac{2-\sqrt{5}}{2+\sqrt{5}}\right)$.

1. + 18

2. -18

3. $18+8\sqrt{5}$

4. $18-8\sqrt{5}$

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.

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

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

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

3. $5+2\sqrt{6}$

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

Q.

Which of the following fractions is equal to $\frac{1}{\sqrt{5}-\sqrt{7}}$?

1. $\frac{-(\sqrt{5}+\sqrt{7})}{8}$

2. $\frac{-(\sqrt{5}+\sqrt{7})}{4}$

3. $\frac{-(\sqrt{5}+\sqrt{7})}{2}$

4. $\frac{-(\sqrt{5}-\sqrt{7})}{2}$

Q.

Find the value of $(\sqrt{2}+\sqrt{2})(\sqrt{2}-\sqrt{2})$.

1. 2
2. 3
3. 0

4. 1

Q.

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

Then a + b is __________.

1. 5

2. 15

3. 10

4. 20

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

Q.

If $x=\sqrt{\frac{5+2\sqrt{6}}{5-2\sqrt{6}}},\text{then}{x}^2(x-10{)}^2=$

1. $5$

2. $5^2$

3. $1$

4. $2^2-1$