Question

rationalise the denominator of 4/2+√3-√7

Answer 1

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Answer 2

Given

• 4/( 2 + √3+√7)  

Steps

4/( 2 + √3+√7)

Multiplying numerator & denominator by (2 + √3) -  √7

= 4 * ( (2 + √3) -  √7 ) / ( 2 + √3+√7) ( (2 + √3) -  √7)

= 4 * ( (2 + √3) -  √7 ) / ( ( 2 + √3)²  - (√7)² )

= 4 * ( (2 + √3) -  √7 ) / ( 4 + 3 + 4√3  - 7 )

= 4 * ( (2 + √3) -  √7 ) / (  4√3  )

=  ( (2 + √3) -  √7 ) /  √3

Multiplying numerator & denominator by  √3

=   ( (2 + √3) -  √7 ) √3 / √3 * √3

= (2√3 + 3 - √21) / 3

=   ( 3 + 2√3 - √21) / 3

4/( 2 + √3+√7)   =  ( 3 + 2√3 - √21) / 3

$\rule{110}2$