Question

simplify.
\sqrt{140}
submit

Explanation:

Step1: Factor 140 into prime factors

We know that \(140 = 4\times35\), and \(4 = 2^2\), \(35=5\times7\). So \(140 = 2^2\times35\).

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

\(\sqrt{140}=\sqrt{2^2\times35}=\sqrt{2^2}\times\sqrt{35}\)

Step3: Simplify \(\sqrt{2^2}\)

Since \(\sqrt{a^2}=a\) for \(a\geq0\), then \(\sqrt{2^2} = 2\). So \(\sqrt{140}=2\sqrt{35}\)

Answer:

\(2\sqrt{35}\)