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.

\( \sqrt{64}= \)

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 $X$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".

Test your knowledge

Question 1

\( \sqrt{36}= \)

Question 2

\( \sqrt{49}= \)

Question 3

Choose the largest value

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

\( \sqrt{121}= \)

Question 2

\( \sqrt{100}= \)

Question 3

\( \sqrt{144}= \)

Choose the largest value

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__

$\sqrt{25}$

$\sqrt{441}=$

The root of 441 is 21.

$21\times21=$

$21\times20+21=$

$420+21=441$

$21$

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

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

$\sqrt{64}=$

8

$\sqrt{36}=$

6

Related Subjects

- Order of Operations: Exponents
- Order of Operations: Roots
- Division and Fraction Bars (Vinculum)
- The Numbers 0 and 1 in Operations
- Neutral Element (Identiy Element)
- Order or Hierarchy of Operations with Fractions
- Exponential Equations
- Multiplicative Inverse
- Integer powering
- Exponents and Roots - Basic
- Exponents and Exponent rules
- Exponents - Special Cases
- Negative Exponents
- Zero Exponent Rule
- Basis of a power
- The exponent of a power
- Power of a Quotient
- Exponent of a Multiplication
- Multiplying Exponents with the Same Base
- Division of Exponents with the Same Base
- Power of a Power
- Powers