# Simplify Squares Roots Worksheets

How to Simplify Square Roots with Negative Numbers We have studied the square roots and are pretty familiar with the positive numbers appearing under the square root symbol. But sometimes we get negative numbers under the radical sign, and things get a bit complicated as we know there aren't any defined square roots of the negative values. However, in some situations, negative radical are easier to solve. For example, 3√-8 can be solved easily. As we all know (-2). (-2). (-2) = -8 and making the answer -2. Particularly in cube roots problems, it is easy to multiply the negative values three times and get a negative answer. Complications arise when we have a problem like √-16. In this problem, there is no way that we can multiply this number with itself and get a negative number. In fact, the square root of a negative number is not possible among the real numbers. To solve this complication, a new number, 'i,' was invented and termed as the imaginary number. The imaginary number 'i' is the square root of the negative number. √-1 = i The imaginary is unique as we square this number; we get a negative number as a result. i2 = (√-1)2 = -1 The simplification of a negative radical is the same as the ordinary radicals but with the minor addition of the imaginary number 'i'. √-16 = √(-1) . 16 = √-1 . √16 = i . √16 = i . 4 = 4i

• ### Basic Lesson

Demonstrates general rules of Simplifying Squares Roots. Simplify the remaining part of the radical.

• ### Intermediate Lesson

Explores how to approach simplifying complex Squares Roots with negative numbers.

• ### Independent Practice 1

Contains 20 Simplify Squares Roots problems. The answers can be found below. Simplify in terms of i.

• ### Independent Practice 2

Features another 20 Simplify Squares Roots problems.

• ### Homework Worksheet

Simplify Squares Roots problems for students to work on at home. Example problems are provided and explained.

• ### Topic Quiz

10 Simplify Squares Roots problems. A math scoring matrix is included.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### That's Learning!

This mathematician has made one of the biggest advancements in human learning by working with logarithms and discovering a method of mechanically multiplying, dividing and taking square and cube roots using what he called "bones." Who is he? Answer: John Napier.