# Square Root of a Negative Number

πPractice square roots

## Square Root of a Negative Number

There is no root of a negative number since any positive number raised to the second power will result in a positive number.

## Test yourself on square roots!

$$\sqrt{64}=$$

## Square Root of a Negative Number

Everything you need to know about the root of negative numbers is that... it simply does not exist!
Negative numbers do not have a root, if in an exam you come across an exercise involving the root of a negative number, your answer should be that it has no solution.
Want to understand the logic? Keep reading.

### What is the root of a number?

The root is some number, let's suppose one that we will call $X$Β that, in fact, will be positive and that, when multiplied by itself will give us $X$.
For example, the root of $100$Β will be a positive number that if we multiply it by itself we will obtain $100$.
That is, $10$.
Instead of saying "multiply it by itself" we can say "raise it to the square".

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### Why does a negative number not have a square root?

As we have seen, the root of any number, for example, $A$ is a positive number that if we square it will give us $A$.
There is no positive number in the whole world that when squared will give us a negative number, therefore, negative numbers do not have a root.

## Exercise Practice

Solve the exercise:
$\sqrt9=3$
If we raise $3$ to the power of two, we will get $9$.
Another exercise
$\sqrt{-9} = No~solution$
We will not be able to find any positive number that, when squared, gives us $-9$ since any positive number squared will be positive and never negative.

Do you know what the answer is?

## Examples with solutions for Square Root of a Negative Number

### Exercise #1

Choose the largest value

### Step-by-Step Solution

Let's calculate the numerical value of each of the roots in the given options:

$\sqrt{25}=5\\ \sqrt{16}=4\\ \sqrt{9}=3\\$and it's clear that:

5>4>3>1 Therefore, the correct answer is option A

$\sqrt{25}$

### Exercise #2

$\sqrt{441}=$

### Step-by-Step Solution

The root of 441 is 21.

$21\times21=$

$21\times20+21=$

$420+21=441$

$21$

### Exercise #3

$(\sqrt{380.25}-\frac{1}{2})^2-11=$

### Step-by-Step Solution

According to the order of operations, we'll first solve the expression in parentheses:

$(\sqrt{380.25}-\frac{1}{2})=(19.5-\frac{1}{2})=(19)$

In the next step, we'll solve the exponentiation, and finally subtract:

$(19)^2-11=(19\times19)-11=361-11=350$

350

### Exercise #4

$\sqrt{64}=$

8

### Exercise #5

$\sqrt{36}=$