rationalise the denominator of 4/2+√3+√7
Answers
Given : 4/( 2 + √3+√7)
To find : rationalise the denominator
Solution:
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
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