Question
Which expression is equivalent to√6 * √15
10√3
3√10
15√6
6√15
10√3
3√10
15√6
6√15
Answers
Answered by
GPT-4o mini
To simplify the expression \( \sqrt{6} \times \sqrt{15} \), you can use the property of square roots that states \( \sqrt{a} \times \sqrt{b} = \sqrt{a \times b} \).
So, we have:
\[
\sqrt{6} \times \sqrt{15} = \sqrt{6 \times 15}
\]
Now, calculate \( 6 \times 15 \):
\[
6 \times 15 = 90
\]
Now, substitute this back into the square root:
\[
\sqrt{90}
\]
Next, simplify \( \sqrt{90} \). We can factor \( 90 \) into its prime factors:
\[
90 = 9 \times 10 = 3^2 \times 10
\]
Now use the square root property:
\[
\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}
\]
So, the expression \( \sqrt{6} \times \sqrt{15} \) simplifies to \( 3\sqrt{10} \).
Thus, the equivalent expression is:
\[
\boxed{3\sqrt{10}}
\]
So, we have:
\[
\sqrt{6} \times \sqrt{15} = \sqrt{6 \times 15}
\]
Now, calculate \( 6 \times 15 \):
\[
6 \times 15 = 90
\]
Now, substitute this back into the square root:
\[
\sqrt{90}
\]
Next, simplify \( \sqrt{90} \). We can factor \( 90 \) into its prime factors:
\[
90 = 9 \times 10 = 3^2 \times 10
\]
Now use the square root property:
\[
\sqrt{90} = \sqrt{9 \times 10} = \sqrt{9} \times \sqrt{10} = 3\sqrt{10}
\]
So, the expression \( \sqrt{6} \times \sqrt{15} \) simplifies to \( 3\sqrt{10} \).
Thus, the equivalent expression is:
\[
\boxed{3\sqrt{10}}
\]
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