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What is the product of 4 and
8sqrt45 in simplest radical form?
Answer:

What is the product of $4$ and $8 \sqrt{45}$ in simplest radical form? $\newline$ Answer:

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Roots of integers

Full solution

Q. What is the product of

4

and

8 \sqrt{45}

in simplest radical form?

\newline

Answer:

Identify Numbers and Operation: Identify the numbers and operation to be performed. $\newline$ We need to multiply $4$ by $8\sqrt{45}$ .
Multiply Whole Numbers: Multiply the whole numbers together. $4 \times 8 = 32$
Write Prime Factorization of $45$ : Write $45$ as a product of its prime factors to simplify the square root. $\newline$ $45 = 9 \times 5 = 3^2 \times 5$
Simplify Square Root: Simplify the square root of $45$ using its prime factorization. $\sqrt{45} = \sqrt{3^2 \times 5} = 3\sqrt{5}$
Multiply Results: Multiply the result from step $2$ with the simplified square root from step $4$ . $\newline$ $32 \times 3\sqrt{5} = 96\sqrt{5}$

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