Question

Simplify square root of 160



2
40
2
40
​



4
10
4
10
​

Answer 1

To simplify \(\sqrt{160}\), we can factor 160 into its prime factors.

First, we find the prime factorization of 160:

\[
160 = 16 \times 10 = 16 \times (2 \times 5) = 16 \times 2 \times 5 = 2^4 \times 5
\]

Now we can rewrite the square root:

\[
\sqrt{160} = \sqrt{2^4 \times 5}
\]

Using the property of square roots that \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), we can separate the factors:

\[
\sqrt{160} = \sqrt{2^4} \times \sqrt{5}
\]

Now simplify \(\sqrt{2^4}\):

\[
\sqrt{2^4} = 2^2 = 4
\]

So, substituting this back in, we have:

\[
\sqrt{160} = 4 \times \sqrt{5}
\]

Thus, the simplified form of \(\sqrt{160}\) is:

\[
4\sqrt{5}
\]