Question

simplifying radicals (guided)
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question
go step by step to reduce the radical.
\sqrt{160}
\sqrt{\square} \sqrt{\square}
answer attempt 1 out of 2
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Explanation:

Step1: Factor the radicand

We need to factor 160 into a product of a perfect square and another number. We know that \(160 = 16\times10\), where 16 is a perfect square (\(4^2 = 16\)).
\[
\sqrt{160}=\sqrt{16\times10}
\]

Step2: Use the property of radicals

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a\geq0\) and \(b\geq0\)), we can split the radical:
\[
\sqrt{16\times10}=\sqrt{16}\times\sqrt{10}
\]

Step3: Simplify the perfect square radical

Since \(\sqrt{16} = 4\) (because \(4^2=16\)), we substitute that in:
\[
\sqrt{16}\times\sqrt{10}=4\sqrt{10}
\]

Answer:

\(4\sqrt{10}\) (or in the boxed form as per the question's structure, the first box is 16, the second box is 10, and the simplified form is \(4\sqrt{10}\); but following the step - by - step, the simplified radical is \(4\sqrt{10}\))