Question

rationalize the denominator of 2 + root 3 upon 2 minus root 3

Answer 1

this is the answer for the given question

Answer 2

Concept-

The conjugate of the binomial (a + b ) is (a - b). If we multiply the denominator by the combined value of the denominator, we will have to multiply the numerator by the same value to avoid changing the value of the expression.

Given-

The expression is given as 2+√3 / 2-√3.

Find-

Rationalize the denominator of 2+√3 / 2-√3

Solution-

⇒ 2 + √3 / 2 - √3

By Rationalizing,

⇒ 2 + √3 / 2 - √3  ×  2 + √3 / 2 + √3

⇒ (2 + √3)² / 2² - (√3)²

⇒ 2² + 2 (2) (√3) + (√3)² / 4 - 3

⇒ 4 + 4√3 + 3 / 1

⇒ 7 + 4√3

Therefore, by rationalizing 2+√3 / 2-√3, we get 7 + 4√3.

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