Simplifying a quotient involving a sum or difference with a square root

Question

simplify:

√8-16/18

Answer 1

To simplify this quotient, we first need to simplify the numerator and the denominator separately:

Numerator:
√8 - 16 = √8 - √(16) = √8 - 4 = 2√2 - 4

Denominator:
18 is already simplified.

Now, combine the simplified numerator and denominator back together:
(2√2 - 4) / 18 = 2(√2 - 2) / 18 = (√2 - 2) / 9

Therefore, (√8 - 16) / 18 simplifies to (√2 - 2) / 9.