Simplify square roots (variables)
Simplify.
Remove all perfect squares from inside the square root.
\[
\sqrt{15 y^{3}}=
\]
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Step 1 ：The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we are asked to simplify the square root of \(15y^{3}\).

Step 2 ：To simplify this, we need to find the perfect squares in the expression under the square root. A perfect square is a number that can be expressed as the product of an integer with itself.

Step 3 ：In this case, the number 15 is not a perfect square, but \(y^{3}\) can be expressed as \(y^{2} * y\), where \(y^{2}\) is a perfect square.

Step 4 ：So, we can simplify the square root of \(15y^{3}\) as the square root of 15 times the square root of \(y^{3}\). The square root of \(y^{3}\) can be further simplified as y times the square root of y.

Step 5 ：So, the simplified form of the square root of \(15y^{3}\) is y times the square root of \(15y\).

Step 6 ：Final Answer: The simplified form of \(\sqrt{15 y^{3}}\) is \(\boxed{y \sqrt{15y}}\).