Question

1/✓3-✓2

rationalise the denominator​

Answer 1

Step-by-step explanation:

Given:-

1/(√3 - √2)

To find:-

Rationalise the denominator.

Solution:-

We have,

1/(√3 - √2)

The denominator = √3 - √2.

We know that

Rationalising factor of √a - √b = √a + √b.

So, Rationalising factor of √3-√2 = √3+√2.

On rationalising the denominator them

→ [1/(√3 - √2)]×[(√3 + √2)/(√3 + √2)]

→ (√3 -√2)/[(√3 - √2)(√3 + √2)]

Consider (√3-√2)(√3+√2) the difference of two squares using the algebraic identity (a-b)(a+b) = a^2 - b^2

Where, we have to put in our expression a = √3 and b = √2.

→ (√3 - √2)/[(√3)^2 - (√2)^2]

→ (√3 - √2)/(3 - 2)

→ (√3 - √2)/ 1

→ √3 - √2

Hence, the denominator is rationalised.

Answer:-

√3 - √2.

Used Formulae:-

Rationalising factor of √a - √b = √a + √b.

(a-b)(a+b) = a^2 - b^2