How does the square root of 27 become 3 times the square root of 3?

Question

5019 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-23T22:34:36

Here's why that happens.

The number #27# can actually be written as

#27 = 3 * 3 * 3#

Alternatively, you can write the same number as

#27 = 3""^2 * 3#

This means that when you take the square root of #27# you can actually apply the product property of radicals, which tells you that

#sqrt(A * B) = sqrt(A) * sqrt(B)#

In your case, you have

#sqrt(27) = sqrt(3""^3 * 3) = sqrt(3""^2) * sqrt(3) = color(green)(3 * sqrt(3))#

This is why the square root of #27# is equal to three times the square root of 3.