Rationalising Factor

Q.

Rationalize the denominator of $\frac{5}{\sqrt{3}-\sqrt{5}}$

1. -5(√3+√5)/2

2. -(√3+√5)/2

3. -5(√3+√5)/4

4. -3(√3+√5)/2

Q.

Find the value of $a$ and $b$ in the following: $\frac{5+2\sqrt{3}}{7+4\sqrt{3}}=a-b\sqrt{3}$

Q.

What is the product of $\frac{1}{8-3\sqrt{7}}$ and its conjugate?

1. 1

2. $8-3\sqrt{7}$

3. $3\sqrt{7}$

4. $8+3\sqrt{7}$

Q.

Find the number of integers x which satisfies the inequality $\frac{3}{1+\sqrt{3}}$ < x < $\frac{3}{\sqrt{5}-\sqrt{3}}$

1. 2

2. 3

3. 4

4. 5

Q. After rationalising the denominator of $\frac{7}{3\sqrt{3}-2\sqrt{2}}$, we get the denominator of the resultant equivalent expression as:

1. $5$
2. $13$
3. $19$
4. $35$

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.

$\frac{1}{2+\sqrt{3}}$ on simplifying is ___

1. $4$

2. $2-\sqrt{3}$

3. $4-\sqrt{3}$

4. $2\sqrt{3}$

Q. Simplify:

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

Q.

Simplify $\frac{1}{2-\sqrt{7}}$ by rationalising the denominator.

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

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

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

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

Q. Rationalise the denominator of $\frac{1}{\sqrt{7}-\sqrt{6}}$.

1. $\sqrt{7}+\sqrt{6}$
2. $\sqrt{7}-\sqrt{6}$
3. $\sqrt{6}-\sqrt{7}$
4. None of these

Q.

Simplify $\frac{5-\sqrt{10}}{5+\sqrt{10}}$ - $\frac{5+\sqrt{10}}{5-\sqrt{10}}$

1. $20\sqrt{10}$

2. 35

3. $\frac{4}{3}\sqrt{10}$

4. -$\frac{4}{3}\sqrt{10}$

Q. If $x=8-\sqrt{60}$, then $\frac{1}{2}[\sqrt{x}+\frac{2}{\sqrt{x}}]=$.....

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

Q. Express as equivalent fractions with rational denominator:
$\frac{\sqrt{10}+\sqrt{5}-\sqrt{3}}{\sqrt{3}+\sqrt{10}-\sqrt{5}}$

Q.

If $x=\sqrt{2}-1(x-\frac{1}{x}{)}^3$ = ______

1. -4

2. -8

3. 4

4. 8

Q. Express as equivalent fractions with rational denominator:
$\frac{1}{1+\sqrt{2}-\sqrt{3}}$

Q. The smallest rationalizing factor of 2$\sqrt{3}$ is

1. $\sqrt{3}$
2. $3\sqrt{3}$
3. $4\sqrt{3}$
4. 0

Q. Which of the following equivalent form of $\frac{3\sqrt{6}-4\sqrt{3}}{4\sqrt{6}-2\sqrt{3}}?$

1. $\frac{8-5\sqrt{2}}{14}$
2. $\frac{5-8\sqrt{2}}{14}$
3. $\frac{8-5\sqrt{2}}{18}$
4. $\frac{5-8\sqrt{2}}{18}$

Q.

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

1. $2$

2. $\frac{21}{11}$

3. $\frac{42}{11}$

4. $1$

Q. If $x=\frac{1}{\sqrt{3}+1}$ then the value of $x+\frac{1}{x}$ is
[2 Marks]

Q. The value of $6+{\log }_{\frac{3}{2}}\left(\frac{1}{3\sqrt{2}}\sqrt{4-\frac{1}{3\sqrt{2}}\sqrt{4-\frac{1}{3\sqrt{2}}\sqrt{4-\frac{1}{3\sqrt{2}}....}}}\right)$.

Q. Express as equivalent fractions with rational denominator:
$\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}-\sqrt{5}}$

Q. Rationalize the denominator of the following
$\left(i\right)\frac{2}{3\sqrt{3}}\left(ii\right)\frac{\sqrt{40}}{\sqrt{3}}\left(iii\right)\frac{4\sqrt{3}+5\sqrt{2}}{\sqrt{48}+\sqrt{18}}$

Q. Find the equivalent form of $\frac{4\sqrt{2}+3\sqrt{6}}{5\sqrt{6}+6\sqrt{2}}$.

1. $\frac{2+21\sqrt{3}}{39}$
2. $\frac{21+2\sqrt{3}}{39}$
3. $\frac{21-2\sqrt{3}}{39}$
4. $\frac{2-21\sqrt{3}}{39}$

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. Express as equivalent fractions with rational denominator:
$\frac{1}{\sqrt{a}+\sqrt{b}+\sqrt{a+b}}$

Q.

Fill in the blanks:

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

Q.

$\frac{\square }{7}=\frac{10}{35}$

Q.

Rationalise the denominator in $\frac{5}{3\sqrt{3}}$

1. $\frac{5\sqrt{5}}{9}$

2. $\frac{5\sqrt{1}}{9}$

3. $\frac{5\sqrt{3}}{3}$

4. $\frac{5\sqrt{3}}{9}$

Q. The value of $6+{\log }_{\frac{3}{2}}(\frac{1}{3\sqrt{2}}\sqrt{4-\frac{1}{3\sqrt{2}}\sqrt{4-\frac{1}{3\sqrt{2}}\sqrt{4-\frac{1}{3\sqrt{2}}}}}.....)$ is

Q. Express as equivalent fractions with rational denominator:
$\frac{(\sqrt{3}+\sqrt{5})(\sqrt{5}+\sqrt{2})}{\sqrt{2}+\sqrt{3}+\sqrt{5}}$