What is SQUARE ROOT OF 3 times the SQUARE ROOT of 21?

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Answer 1 · 2015-09-06T11:44:43

$sqrt(3) * sqrt(21) = 3sqrt(7)$

You know that for real, positive numbers you have

$color(blue)(sqrt(a) * sqrt(b) = sqrt(a * b)$

This means that you can write

$sqrt(3) * sqrt(21) = sqrt(3 * 21)$

If you write $21$ as the product of its prime factors $3$ and $7$ , you can say that

$sqrt(3 * 21) = sqrt(3 * 3 * 7) = sqrt(9 * 7)$

Now use the same multiplication property of radicals to write

$sqrt(9 * 7) = sqrt(9) * sqrt(7) = 3 * sqrt(7) = color(green)(3sqrt(7)$