Questions: Simplify. [ sqrt20 y sqrt5 y^2 ]

Simplify. [ sqrt20 y sqrt5 y^2 ]
Transcript text: Simplify. \[ \sqrt{20 y} \sqrt{5 y^{2}} \]
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Solution

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Solution Steps

Step 1: Rewrite the expression using the product rule for square roots

\[ \sqrt{20y} \cdot \sqrt{5y^2} = \sqrt{(20y) \cdot (5y^2)} \]

Step 2: Multiply the terms inside the square root

\[ \sqrt{(20y) \cdot (5y^2)} = \sqrt{100y^3} \]

Step 3: Simplify the square root

\[ \sqrt{100y^3} = \sqrt{100} \cdot \sqrt{y^3} = 10 \cdot y^{3/2} \]

Final Answer

\(\boxed{10y^{3/2}}\)

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