How do you simplify #\sqrt{20}# without using a calculator?

1 Answer
Apr 18, 2018

Answer:

#2sqrt5#

Here's how I did it:

Explanation:

#quadquadsqrt20#

First, find a factor of #20# that can be square rooted into a whole number. That number is #4#:
#quadquadsqrt(4 * 5)#

#quadquadsqrt4 * sqrt5#

We know that the #sqrt4 = 2#:
#quadquad2 * sqrt5#

Combine it:
#quadquad2sqrt5#

If you actually needed to find the decimal value of this problem, you will need to use the calculator. If you plug it into the calculator, you will get #~~4.472# (rounded to the thousandth's place).

Hope this helps!