Question

simplify.
10√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 10

Now we have \(10\times3\sqrt{5}\). Multiplying 10 and 3 gives \(30\), so the simplified form is \(30\sqrt{5}\).

Answer:

\(30\sqrt{5}\)