Question
factor each square root
square root of 160
square root of 160
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GPT-4o mini
To factor the square root of 160, we start by simplifying the expression \( \sqrt{160} \).
1. First, we find the prime factorization of 160:
\[
160 = 16 \times 10 = 16 \times (2 \times 5) = 2^4 \times 5
\]
2. Now, we can rewrite \( \sqrt{160} \) using this factorization:
\[
\sqrt{160} = \sqrt{2^4 \times 5}
\]
3. We can utilize the property of square roots that states \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \):
\[
\sqrt{160} = \sqrt{2^4} \times \sqrt{5}
\]
4. Now we simplify \( \sqrt{2^4} \):
\[
\sqrt{2^4} = 2^2 = 4
\]
5. Substituting back, we have:
\[
\sqrt{160} = 4 \times \sqrt{5}
\]
Thus, the simplified form of \( \sqrt{160} \) is:
\[
\sqrt{160} = 4\sqrt{5}
\]
1. First, we find the prime factorization of 160:
\[
160 = 16 \times 10 = 16 \times (2 \times 5) = 2^4 \times 5
\]
2. Now, we can rewrite \( \sqrt{160} \) using this factorization:
\[
\sqrt{160} = \sqrt{2^4 \times 5}
\]
3. We can utilize the property of square roots that states \( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \):
\[
\sqrt{160} = \sqrt{2^4} \times \sqrt{5}
\]
4. Now we simplify \( \sqrt{2^4} \):
\[
\sqrt{2^4} = 2^2 = 4
\]
5. Substituting back, we have:
\[
\sqrt{160} = 4 \times \sqrt{5}
\]
Thus, the simplified form of \( \sqrt{160} \) is:
\[
\sqrt{160} = 4\sqrt{5}
\]
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