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

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

Choose the largest value

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.

The root is some number, let's suppose one that we will call $X$ that, in fact, will be positive and that, when multiplied by itself will give us $X$.

For example, the root of $100$ 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".

Test your knowledge

Question 1

\( \sqrt{64}= \)

Question 2

\( \sqrt{36}= \)

Question 3

\( \sqrt{49}= \)

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.

**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?

Question 1

Solve the following exercise:

\( \sqrt{x^2}= \)

Question 2

\( 5+\sqrt{36}-1= \)

Question 3

\( \sqrt{441}= \)

Related Subjects

- Powers
- Division of Exponents with the Same Base
- Power of a Quotient
- Power of a Power
- Multiplying Exponents with the Same Base
- Exponent of a Multiplication
- Exponents for Seventh Graders
- The exponent of a power
- Order of Operations: (Exponents)
- Exponential Equations
- Multiplicative Inverse
- Order or Hierarchy of Operations with Fractions