Rationalise the denominator and simplify:

(i) √3+1
/ 2√2− √3​

2 thoughts on “Rationalise the denominator and simplify:<br /><br />(i) √3+1<br /> / 2√2− √3​”

1. 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.

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2. 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:

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