Questions: Simplify. 8 sqrt(45)

Simplify. 8 sqrt(45)
Transcript text: Simplify. \[ 8 \sqrt{45} \] $\square$ Submit
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Solution

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Solution Steps

Step 1: Factor the Radicand

First, factor the number inside the square root (the radicand) into its prime factors: \[ 45 = 9 \times 5 = 3^2 \times 5 \]

Step 2: Apply the Square Root Property

Use the property of square roots that allows you to separate the factors: \[ \sqrt{45} = \sqrt{3^2 \times 5} = \sqrt{3^2} \times \sqrt{5} = 3\sqrt{5} \]

Step 3: Multiply by the Coefficient

Multiply the simplified square root by the coefficient outside the square root: \[ 8 \sqrt{45} = 8 \times 3\sqrt{5} = 24\sqrt{5} \]

Final Answer

\( \boxed{24\sqrt{5}} \)

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