# What is the square root of 4?

Sep 6, 2015

2 and -2 are square roots of 4. The principal square root of $4$, (denoted $\sqrt{4}$) is $2$

#### Explanation:

A number is a square root of 4 is, when multiplied by itself, the result is 4.

In notation: $n$ is a square root of $4$ if ${n}^{2} = n \times n = 4$

There are two numbers that will work $2 \times 2 = 4$ and also $- 2 \times - 2 = 4$ so the numbers $2$ and $- 2$ are square roots of $4$. When people talk about the square root of $4$, they usually mean the number whose complete name is "the principal square root of $4$.

The principal square root of a (positive) number is the non-negative square root. The symbol $\sqrt{_}$ denoted the principal square root.

So $\sqrt{4} = 2$

Here on Socratic to type $\sqrt{4}$ use the hashtag # before and after sqrt4. I you want some arithmetic under the square root symbol, use parentheses:

no parentheses: hashtag sqrt9+16 hashtag gets $\sqrt{9} + 16$

With parentheses hashtag sqrt(9+16) hashtag gets $\sqrt{9 + 16}$