Simplifying Square Roots

Using Perfect Square Factors

Review

Square and square root – inverse operations

Ex. 1: √25 = 5, since 52 = 25 Ex. 2: √529 = 23, since 232 = 529

Terms Used with Radicals

The √ symbol is called the radical signThe root being taken (usually 2 – unwritten

– for a square root) is the indexThe number inside the radical is the

radicand

√25(2)

Perfect Square Factors

Simplify perfect square factors of the radicand

Ex. 1: √12 = √4∙3 = 2√3Ex. 2: √32 = √16∙2 = 4√2Ex. 3: 3√8 = 3√4∙2 = 3∙2√2 = 6√2

Practice Problem

Now try this Problem: Simplify √48

Solution:√48 = √16∙3 = 4√3

OR:√48 = √4∙12 = 2√12 = 2√4∙3 = 2∙2√3 = 4√3

Now Try These

Hint: Look for factors of 4, 9, 25, or 49

1. Simplify √18

2. Simplify √27

3. Simplify 2√75

4. Simplify √98(answers on the next slide)

Answers to previous problems

1. √18 = 3√2 (click here to see the solution)

2. √27 = 3√3 (click here to see the solution)

3. 2√75 = 10√3 (click here to see the solution)

4. √98 = 7√2 (click here to see the solution)

The End

Did you miss any of the previous problems? If so, try them again.

Then continue with the next content item of the lesson!

Solution for √18

√18 = √9 ∙2 = 3√2

Back

Solution for √27

√27 = √9 ∙3 = 3√3

Back

Solution for 2√75

2√75 = 2√25∙3 = 2∙5√3 = 10√3

Back

Solution for √98

√98 = √49 ∙2 = 7√2

Back