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

1 Answer
Sep 6, 2015

Answer:

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

Explanation:

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)#