How Do You Simplify the Square Root of a Negative Number?

How Do You Simplify the Square Root of a Negative Number?

Note:

Simplifying the square root of a negative number is very similar to simplifying the square root of a positive number. You just need to remember 'i' in your answer! Check out this tutorial to see how to simplify the square root of a negative number.

Keywords:

problem

simplify

square roots

negative numbers

imaginary numbers

i

radicals

Background Tutorials

Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Anytime you square an integer, the result is a perfect square! The numbers 4, 9, 16, and 25 are just a few perfect squares, but there are infinitely more! Check out this tutorial, and then see if you can find some more perfect squares!

Interpret parts of an expression, such as terms, factors, and coefficients.

You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!

Factors are a fundamental part of algebra, so it would be a great idea to know all about them. This tutorial can help! Take a look!

Further Exploration

Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

The solution to a quadratic equation can sometimes be an imaginary number! This tutorial shows you how to use the square root method to solve a quadratic equation that has imaginary solutions.