Question

Rationalise the denominator and simplify:

(i) √3+1
/ 2√2− √3​

Answer 1

Answer:

Given √3+1/√3-1

We need to rationalize the givenequation

To rationalize we will multiply and divide the denominator by √3+1

(√3+1)√3+1)/(√3-1)(√3+1)

Denominator can be simplified using the identity (a2-b2)=(a-b)(a+b)

And the equation becomes

=(√3+1)2/(√3)2-(1)2

=(4+2√3)/2

=2+√3

Step-by-step explanation:

Answer 2

Solution!!

(√3 + 1)/(2√2 - √3)

Expand the expression by multiplying.

= (√3 + 1)/(2√2 - √3) × (2√2 + √3)/(2√2 + √3)

= [(√3 + 1)(2√2 + √3)]/[2√2 - √3)(2√2 + √3)]

Simplify the denominator by using (a - b)(a + b) = a² - b².

= [(√3 + 1)(2√2 + √3)]/[(2√2)² - (√3)²]

= [(√3 + 1)(2√2 + √3)]/[8 - 3]

= [(√3 + 1)(2√2 + √3)]/5

Multiplying the expressions in the numerator.

= (2√6 + 3 + 2√2 + √3)/5

Hence, we have got our answer after rationalising the denominator and simplifying the expressions.