Question

rationalise the denominator of 1/4+2√3​

Answer 1

hence required answer is 2 minus root 3 upon 2

Answer 2

Concept

A radical or imaginary number can be removed from the denominator of an algebraic fraction by a procedure known as rationalization. That is, eliminate the radicals from a fraction to leave only a rational integer in the denominator.

Given

the expression is 1/4₊2√3

Find

we need to rationalize the denominator of the above expression.

Solution

The process of rationalizing an expression is removing any surplus from the fractions' lowest part (denominator). Usually, when someone asks you to simplify a term, they also mean that you should rationalize it.

1/4₊2√3 × 4₋2√3/4₋2√3

=  4₋2√3 / (4)² ₋ (2√3)²

=  4₋2√3/16 ₋ (2√3)²

= 4₋2√3/16 ₋ 4 × 3

=  4₋2√3/16 ₋ 12

= 2(2₋ √3)/4

= 2₋ √3/2

hence after rationalizing the denominator we get he answer as  2₋ √3/2

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