# What is the square root of 164 simplified in radical form?

May 24, 2017

$2 \sqrt{41}$

#### Explanation:

Step 1. Find all the factors of $164$
$164 = 2 \cdot 82 = 2 \cdot 2 \cdot 41 = {2}^{2} \cdot 41$

[$41$ is a prime number]

Step 2. Evaluate the square root
$\sqrt{164} = \sqrt{{2}^{2} \cdot 41} = 2 \sqrt{41}$

May 24, 2017

$2 \sqrt{41}$

#### Explanation:

We can think of two numbers that multiply to $164$. If we divide $164$ by $4$ we get $41$. We can write an expression like this:

$\sqrt{4} \cdot \sqrt{41} = \sqrt{164}$

If we look closely, we can see that we have a $\sqrt{4}$ and so we can simplify it by saying $\sqrt{4} = 2$.

Rewriting the expression:

$2 \cdot \sqrt{41} = \sqrt{164}$

So the $\sqrt{164}$ can be simplified to $2 \sqrt{41}$ in radical form.

The goal of these problems is to break down the radical using at least one perfect square (e.g $4 , 9 , 16 , 25 , 36 , 49$.etc) which is why I chose $4$ because you can easily find the square root of $4$.