R.D. Sharma solutions for Mathematics [English] Class 9 chapter 3 - Rationalisation [Latest edition]

Simplify of the following:

`root(3)4  xx root(3)16`

Simplify of the following:

`root(4)1250/root(4)2`

Simplify the following expressions:

`(4 + sqrt7)(3 + sqrt2)`

Simplify the following expressions:

`(3 + sqrt3)(5 - sqrt2)`

Simplify the following expressions:

`(sqrt5 - 2)(sqrt3 - sqrt5)`

Simplify the following expressions:

`(11 + sqrt11)(11 - sqrt11)`

Simplify the following expressions:

`(5 + sqrt7)(5 - sqrt7)`

Simplify the following expressions:

`(sqrt8 - sqrt2)(sqrt8 + sqrt2)`

Simplify the following expressions:

`(3 + sqrt3)(3 - sqrt3)`

Simplify the following expression:

`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`

Simplify the following expressions:

`(sqrt3 + sqrt7)^2`

Simplify the following expressions:

`(sqrt5 - sqrt3)^2`

Simplify the following expressions:

`(2sqrt5 + 3sqrt2)^2`

Rationalise the denominator of each of the following

`3/sqrt5`

Rationalise the denominator of the following:

`3/(2sqrt5)`

Rationalise the denominator of each of the following 

`1/sqrt12`

Rationalise the denominator of the following

`sqrt2/sqrt5`

Rationalise the denominator of the following

`(sqrt3 + 1)/sqrt2`

Rationalise the denominator of the following

`(sqrt2 + sqrt5)/3`

Rationalise the denominator of the following 

`(3sqrt2)/sqrt5`

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`2/sqrt3`

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`3/sqrt10`

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`(sqrt5 + 1)/sqrt2`

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`(sqrt10 + sqrt15)/sqrt2`

`

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`(2 + sqrt3)/3`

Find the value to three places of decimals of the following. It is given that

`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`

`(sqrt2 - 1)/sqrt5`

Express the following with rational denominator:

`1/(3 + sqrt2)`

Express of the following with rational denominator:

`1/(sqrt6 - sqrt5)`

Express the following with rational denominator:

`16/(sqrt41 - 5)`

Express the following with rational denominator:

`30/(5sqrt3 - 3sqrt5)`

Express the following with rational denominator:

`1/(2sqrt5 - sqrt3)`

Express the following with rational denominator:

`(sqrt3 + 1)/(2sqrt2 - sqrt3)`

Express the following with rational denominator:

`(6 - 4sqrt2)/(6 + 4sqrt2)`

Express the following with rational denominator:

`(3sqrt2 + 1)/(2sqrt5 - 3)`

Express each one of the following with rational denominator:

`(b^2)/(sqrt(a^2 + b^2) + a)`

Rationales the denominator and simplify:

`(3 - sqrt2)/(3 + sqrt2)`

Rationales the denominator and simplify:

`(5 + 2sqrt3)/(7 + 4sqrt3)`

Rationales the denominator and simplify:

`(1 + sqrt2)/(3 - 2sqrt2)`

Rationales the denominator and simplify:

`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`

Rationales the denominator and simplify:

`(4sqrt3 + 5sqrt2)/(sqrt48 + sqrt18)`

Rationales the denominator and simplify:

`(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3)`

Simplify:

`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`

Simplify

`1/(2 + sqrt3) + 2/(sqrt5 - sqrt3) + 1/(2 - sqrt5)`

Simplify:

`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`

In the following determine rational numbers a and b:

`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`

In the following determine rational numbers a and b:

`(4 + sqrt2)/(2 + sqrt2) = n - sqrtb`

In the following determine rational numbers a and b:

`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`

In the following determine rational numbers a and b:

`(5 + 3sqrt3)/(7 + 4sqrt3) = a + bsqrt3`

In the following determine rational numbers a and b:

`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) = a - bsqrt77`

In the following determine rational numbers a and b:

`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`

Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and  `sqrt5 = 2.236`

Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`

`(3 - sqrt5)/(3 + 2sqrt5)`

Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`

`(1 + sqrt2)/(3 - 2sqrt2)`

Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]

Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]

if `x = 2 +  sqrt3`,find the value of `x^2 + 1/x^2`

if   `x= 3 + sqrt8`, find the value of `x^2 + 1/x^2`

if `x =  (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7` 

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

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

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

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

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

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

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

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

Simplify \[\sqrt{3 + 2\sqrt{2}}\].

Simplify \[\sqrt{3 - 2\sqrt{2}}\].

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

\[\sqrt{10} \times \sqrt{15}\] is equal to

\[\sqrt[5]{6} \times \sqrt[5]{6}\] is equal to

The rationalisation factor of \[\sqrt{3}\] is 

The rationalisation factor of \[2 + \sqrt{3}\] is 

If x = \[\sqrt{5} + 2\],then \[x - \frac{1}{x}\] equals

If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then

The simplest rationalising factor of  \[\sqrt[3]{500}\] is 

The simplest rationalising factor of \[\sqrt{3} + \sqrt{5}\] is ______.

The simplest rationalising factor of \[2\sqrt{5}-\]\[\sqrt{3}\] is 

If x = \[\frac{2}{3 + \sqrt{7}}\],then (x−3)² =

If \[x = 7 + 4\sqrt{3}\] and xy =1, then \[\frac{1}{x^2} + \frac{1}{y^2} =\]

If \[x + \sqrt{15} = 4,\] then \[x + \frac{1}{x}\] = 

If \[x = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}\] and \[y = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}\] then x + y +xy=

If x= \[\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}\] and y = \[\frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}\] , then x² + y +y² =

\[\frac{1}{\sqrt{9} - \sqrt{8}}\] is equal to

The value of \[\frac{\sqrt{48} + \sqrt{32}}{\sqrt{27} + \sqrt{18}}\] is 

If \[\frac{5 - \sqrt{3}}{2 + \sqrt{3}} = x + y\sqrt{3}\] , then

If x = \[\sqrt[3]{2 + \sqrt{3}}\] , then \[x^3 + \frac{1}{x^3} =\]

The value of \[\sqrt{3 - 2\sqrt{2}}\] is 

The value of \[\sqrt{5 + 2\sqrt{6}}\] is

If \[\sqrt{2} = 1 . 4142\] then \[\sqrt{\frac{\sqrt{2} - 1}{\sqrt{2} + 1}}\] is equal to

If \[\sqrt{2} = 1 . 414,\] then the value of \[\sqrt{6} - \sqrt{3}\] upto three places of decimal is

The positive square root of \[7 + \sqrt{48}\] is 

If \[x = \sqrt{6} + \sqrt{5}\],then \[x^2 + \frac{1}{x^2} - 2 =\]

If \[\sqrt{13 - a\sqrt{10}} = \sqrt{8} + \sqrt{5}, \text { then a } =\]