Question

simplify.
\sqrt{148}

Explanation:

Step1: Factor 148 into prime factors

First, we find the prime factorization of 148. We start by dividing by the smallest prime numbers. 148 divided by 2 is 74, and 74 divided by 2 is 37. So, \(148 = 2\times2\times37=2^{2}\times37\).

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

We can rewrite \(\sqrt{148}\) as \(\sqrt{2^{2}\times37}\). Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\), we get \(\sqrt{2^{2}\times37}=\sqrt{2^{2}}\times\sqrt{37}\).

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

Since \(\sqrt{a^{2}} = a\) for \(a\geq0\), \(\sqrt{2^{2}}=2\). So, \(\sqrt{2^{2}}\times\sqrt{37}=2\sqrt{37}\).

Answer:

\(2\sqrt{37}\)