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

Apr 18, 2018

$2 \sqrt{5}$

Here's how I did it:

Explanation:

$\quad \quad \sqrt{20}$

First, find a factor of $20$ that can be square rooted into a whole number. That number is $4$:
$\quad \quad \sqrt{4 \cdot 5}$

$\quad \quad \sqrt{4} \cdot \sqrt{5}$

We know that the $\sqrt{4} = 2$:
$\quad \quad 2 \cdot \sqrt{5}$

Combine it:
$\quad \quad 2 \sqrt{5}$

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 $\approx 4.472$ (rounded to the thousandth's place).

Hope this helps!