Question

Rationalize the denominator.

2 / squareroot7+squareroot3

Please show steps

Answer 1

remember that (a-b)(a+b) = a^2 - b^2

so, (√7 - √3)(√7 + √3) = 7 - 3 = 4

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