Simplify √18a- √72a.

Question

Please show the work involved in solving this question.

Answer 1

The first step is to find the factors of 18, and the factors of 72, and to identify squares in the factors.

18 = 2•3²

72 = 2³•3² = 2•2²•3²

Next, simplify √18 and √72

√18 = √2•√3² = √2 • 3 = 3√2

√72 = √2•√2²•√3² = √2 • 2 • 3 = 6√2

Now, use the simplified square roots to rewrite the expression.

√18a - √72a = 3√2a - 6√2a = -3√2a