Question

square root of 5 times square root of 15 simplified

Answer 1

To simplify the expression \(\sqrt{5} \times \sqrt{15}\), you can use the property of square roots that states \(\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}\).

So, we have:

\[
\sqrt{5} \times \sqrt{15} = \sqrt{5 \times 15}
\]

Calculating \(5 \times 15\):

\[
5 \times 15 = 75
\]

Now we can write:

\[
\sqrt{5} \times \sqrt{15} = \sqrt{75}
\]

Next, we simplify \(\sqrt{75}\). We can factor \(75\) into \(25 \times 3\):

\[
75 = 25 \times 3
\]

Now, taking the square root of \(75\):

\[
\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}
\]

Thus, the simplified form of \(\sqrt{5} \times \sqrt{15}\) is:

\[
5\sqrt{3}
\]