Question

simplify. 8√220

Explanation:

Step1: Factor 220

Factor 220 into prime factors: \(220 = 4\times55\), and \(4 = 2^2\). So, \(\sqrt{220}=\sqrt{4\times55}\).

Step2: Use square - root property

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\)), we have \(\sqrt{4\times55}=\sqrt{4}\times\sqrt{55}\). Since \(\sqrt{4} = 2\), then \(\sqrt{220}=2\sqrt{55}\).

Step3: Multiply by 8

Now, multiply by 8: \(8\sqrt{220}=8\times2\sqrt{55}\).

Step4: Calculate the product

\(8\times2 = 16\), so \(8\sqrt{220}=16\sqrt{55}\).

Answer:

\(16\sqrt{55}\)