Question

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

Answer 1

`2sqrt(41)`

Explanation:

Step 1. Find all the factors of `164`
`164=2*82=2*2*41=2^2*41`

[`41` is a prime number]

Step 2. Evaluate the square root
`sqrt(164)=sqrt(2^2*41)=2sqrt(41)`

Answer 2

`2sqrt41`

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)*sqrt(41)=sqrt(164)`

If we look closely, we can see that we have a `sqrt4` and so we can simplify it by saying `sqrt4=2`.

Rewriting the expression:

`2*sqrt41=sqrt164`

So the `sqrt164` can be simplified to `2sqrt41` 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`.