How do you rationalize the denominator and simplify 5 / ( sqrt 14 - 2 )?

1 Answer
Apr 8, 2016

(sqrt14 + 2)/2 = sqrt14/2 + 1

Explanation:

By rationalizing a fraction, we mean removing any irrational values from the denominator, without changing the fraction.

Here, we have to remove sqrt14 from the denominator, without changing the value of the expression.

We know that a^2-b^2 =(a+b)(a-b)

We have sqrt14-2 as the denominator. To remove the square root, we must multiply the denominator by sqrt14+2

Dividing and multiplying a fraction by the same number does not change the fraction.

5/(sqrt14 -2) xx (sqrt14+2)/(sqrt14 + 2)

(5 xx (sqrt14+2))/((sqrt14 -2)(sqrt14 + 2))

(5sqrt14 + 10)/((sqrt14)^2 - 2^2)

(5sqrt14 + 10)/(14 -4) =(5sqrt14 + 10)/10

5 is the common factor of the numerator.

(5(sqrt14 + 2))/10

Cancel 5 from the numerator and denominator.

(sqrt14 + 2)/2 = sqrt14/2 + 1