# What is the square root of 83?

Sep 21, 2015

Some number between 9 and 10.

#### Explanation:

$\sqrt{83}$ is an irrational number. You won't be able to simplify it any further either, since it doesn't have any perfect square factors.

However, you will be able to tell between which two numbers it lies in. ${9}^{2}$ is $81$ and ${10}^{2}$ is $100$. Therefore, you can say that a certain number between 9 and 10 is 83 when squared.

If you're looking for an exact answer, then it will be 9.11043357914... (I got that using a calculator).

Sep 21, 2015

Symbolically, $\sqrt{83}$ can't be simplified because has no factors that are perfect squares (other than 1) -- in fact, it's a prime number. Of course, you can approximate with your calculator: $\sqrt{83} \approx 9.110433579$