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What is the product of
10sqrt8 and
4sqrt12 in simplest radical form?
Answer:

What is the product of $10 \sqrt{8}$ and $4 \sqrt{12}$ in simplest radical form? $\newline$ Answer:

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Simplify radical expressions: mixed review

Full solution

Q. What is the product of

10 \sqrt{8}

and

4 \sqrt{12}

in simplest radical form?

\newline

Answer:

Write Expression: Write down the expression to be simplified. $\newline$ We need to find the product of $10\sqrt{8}$ and $4\sqrt{12}$ .
Multiply Coefficients and Radicands: Multiply the coefficients (numbers outside the square roots) and the radicands (numbers inside the square roots) separately. $10\sqrt{8} \times 4\sqrt{12} = (10 \times 4) \times (\sqrt{8} \times \sqrt{12})$
Calculate Product of Coefficients: Calculate the product of the coefficients. $10 \times 4 = 40$
Combine Radicands: Use the property of radicals that $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$ to combine the radicands. $\sqrt{8} \times \sqrt{12} = \sqrt{8 \times 12}$
Calculate Product of Radicands: Calculate the product of the radicands. $8 \times 12 = 96$
Combine Coefficient and Radicand: Combine the coefficient and the radicand. $40 \times \sqrt{96}$
Simplify Square Root: Simplify the square root by finding the prime factors of the radicand. $\sqrt{96} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 3} = \sqrt{2^5 \times 3}$
Group Identical Factors: Group the identical factors and use the property that $\sqrt{a^2} = a$ . $\sqrt{2^5 \times 3} = \sqrt{2^4 \times 2 \times 3} = \sqrt{2^4} \times \sqrt{2 \times 3}$
Simplify Perfect Square: Simplify the square root of the perfect square and the remaining radicand. $\sqrt{2^4} \times \sqrt{2 \times 3} = 2^2 \times \sqrt{2 \times 3} = 4 \times \sqrt{6}$
Multiply Simplified Square Root: Multiply the simplified square root by the coefficient. $\newline$ $40 \times 4 \times \sqrt{6} = 160 \times \sqrt{6}$

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\newline

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\newline

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Question

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\newline

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