RD Sharma 2020 solution class 9 chapter 3 Rationalisation VSAQS

VSAQS

Page-3.19

Question 1:

Write the value of $\left(2+\sqrt{3}\right) \left(2-\sqrt{3}\right).$

Answer 1:

Given that 

It can be simplified as 

Hence the value of the given expression is.

Question 2:

Write the reciprocal of $5+\sqrt{2}$.

Answer 2:

Given that, it’s reciprocal is given as 

It can be simplified by rationalizing the denominator. The rationalizing factor of is, we will multiply numerator and denominator of the given expression by, to get

Hence reciprocal of the given expression is.

Question 3:

Write the rationalisation factor of $7-3\sqrt{5}$.

Answer 3:

The rationalizing factor of is. Hence the rationalizing factor of is .

Question 4:

If $\frac{\sqrt{3}-1}{\sqrt{3}+1}=x+y\sqrt{3},$find the values of x and y.

Answer 4:

It is given that;

.we need to find x and y

We know that rationalization factor for is . We will multiply numerator and denominator of the given expression by, to get

On equating rational and irrational terms, we get 

Hence, we get.

Question 5:

If x=$\sqrt{2}-1$, then write the value of $\frac{1}{x}.$

Answer 5:

Given that.Hence is given as

We know that rationalization factor for is . We will multiply each side of the given expression by, to get

Hence the value of the given expression is.

Question 6:

If $a=\sqrt{2}+1$, then find the value of $a-\frac{1}{a}$.

Answer 6:

Given that, hence is given as

.we are asked to find

We know that rationalization factor for is . We will multiply each side of the given expression by, to get

Therefore,

Hence value of the given expression is.

Question 7:

If $x=2+\sqrt{3}$,  find the value of $x+\frac{1}{x}$.

Answer 7:

Given that, hence $\frac{1}{x}$is given as

.We are asked to find

We know that rationalization factor for is . We will multiply each side of the given expression by, to get

Therefore,

Hence value of the given expression is.

Question 8:

Write the rationalisation factor of $\sqrt{5}-2$.

Answer 8:

Given that, we know that rationalization factor of is

So the rationalization factor of is.

Question 9:

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

Answer 9:

We are asked to simplify. It can be written in the form as

Hence the value of given expression is.

Question 10:

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

Answer 10:

We are asked to simplify. It can be written in the form as

Hence the value of the given expression is.

Question 11:

If $x= 3+2\sqrt{2}$, then find the value of $\sqrt{x}-\frac{1}{\sqrt{x}}$.

Answer 11:

Given that:.It can be written in the form as

Therefore,

We know that rationalization factor for is . We will multiply numerator and denominator of the given expression by, to get

Hence,

Therefore, value of the given expression is.