Question

simplify.
$5\sqrt{45}$

Explanation:

Step1: Factor 45 into prime factors

We know that \(45 = 9\times5\), and \(9 = 3^2\). So we can rewrite \(\sqrt{45}\) as \(\sqrt{9\times5}\).

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0,b\geq0\))

\(\sqrt{9\times5}=\sqrt{9}\times\sqrt{5}\). Since \(\sqrt{9} = 3\), this becomes \(3\sqrt{5}\).

Step3: Multiply by the coefficient outside the square root

We have \(5\sqrt{45}=5\times3\sqrt{5}\).

Step4: Calculate the product of the coefficients

\(5\times3 = 15\), so \(5\sqrt{45}=15\sqrt{5}\).

Answer:

\(15\sqrt{5}\)