Question

Simplify the expression:
(6/(√36 + √27)) + (6/(√27 + √18)) + (6/(√18 + √9))

Answer 1

2

Explanation:

Answer 2

9514 1404 393

Answer:

2

Explanation:

A calculator can give you the answer quickly: 2.

__

Working this out in detail is a little more complicated. Eliminating roots in the denominator means multiplying numerator and denominator by the "conjugate" of the denominator.

`(6)/(√(36)+√(27))+(6)/(√(27)+√(18))+(6)/(√(18)+√(9))\\\\=6\left((6-3√(3))/(36-27)+(3(√(3)-√(2)))/(27-18)+(3(√(2)-1))/(18-9)\right)\\\\=(6)/(9)(6-3√(3)+3√(3)-3√(2)+3√(2)-3)=(2)/(3)\cdot 3=\boxed{2}`