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

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

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Answer 1 · 2016-03-29T13:57:34

$\pm 3 \sqrt{7}$ $+-3sqrt(7)$

Explanation:

Notice that $3 \times 7 = 21$ $3xx7=21$

Write as: $\sqrt{3 \times 7} \times \sqrt{3}$ $" "sqrt(3xx7)xxsqrt(3)$

This is the same as

$\sqrt{3} \times \sqrt{7} \times \sqrt{3}$ $" "sqrt(3)xxsqrt(7)xxsqrt(3)$

Which is the same as

${(\sqrt{3})}^{2} \times \sqrt{7}$ $" "(sqrt(3))^2xxsqrt(7)$

$3 \sqrt{7}$ $" "3sqrt(7)$

'~~~~~~~~~~~~~~~~~~~~~~
Note that if $\sqrt{3}$ $sqrt(3)$ is negative then ${(\sqrt{3})}^{2}$ $(sqrt(3))^2$ is positive so the 3 is definitely positive.

However, $\sqrt{7}$ $sqrt(7)$ stands on its own so we have $\pm \sqrt{7}$ $+-sqrt(7)$

Thus $3 \sqrt{7} is more correctly written as \pm 3 \sqrt{7}$ $3sqrt(7)" is more correctly written as "+-3sqrt(7)$

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

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