How do you simplify $\sqrt{3} \sqrt{21}$ $sqrt3sqrt21$ ?

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How do you simplify $\sqrt{3} \sqrt{21}$ $sqrt3sqrt21$ ?

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Answer 1 · 2018-05-01T10:12:58

I get $3 \sqrt{7}$ $3\sqrt{7}$ , see below.

Explanation:

Factor the 21 and write each factor as its own square toot:

$21 = 3 \times 7$ $21=3×7$ so $\sqrt{21} = \sqrt{3} \times \sqrt{7}$ $\sqrt{21}=\sqrt{3}×\sqrt{7}$

You Can't do this with the $\sqrt{3}$ $\sqrt{3}$ factor because 3 is,already prime. But you can find a pair of like square roots now in the product $\sqrt{3} \sqrt{21}$ $\sqrt{3}\sqrt{21}$ :

$\sqrt{3} \sqrt{21} = \sqrt{3} \times (\sqrt{3} \times \sqrt{7})$ $\sqrt{3}\sqrt{21}=\sqrt{3}×(\sqrt{3}×\sqrt{7})$

$= (\sqrt{3} \times \sqrt{3}) \times \sqrt{7}$ $=(\sqrt{3}×\sqrt{3})×\sqrt{7}$

$= {(\sqrt{3})}^{2} \times \sqrt{7}$ $=(\sqrt{3})^2×\sqrt{7}$

$= 3 \sqrt{7}$ $=color(blue)(3\sqrt{7})$

Answer 2 · 2018-05-01T10:25:16

$3 \sqrt{7}$ $3sqrt7$

Explanation:

$using the law of radicals$ $"using the "color(blue)"law of radicals"$

$∙ x \sqrt{a} \times \sqrt{b} \Leftrightarrow \sqrt{a b}$ $•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)$

$\Rightarrow \sqrt{3} \times \sqrt{21} = \sqrt{3 \times 21} = \sqrt{63}$ $rArrsqrt3xxsqrt21=sqrt(3xx21)=sqrt63$

$\sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} = 3 \sqrt{7}$ $sqrt63=sqrt(9xx7)=sqrt9xxsqrt7=3sqrt7$

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How do you simplify $\sqrt{3} \sqrt{21}$ $sqrt3sqrt21$ ?

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