Algebra Review: Square Roots and Radicals

For Use With Lesson 4-5

A radical symbol  indicates a square root. In general, x 2 = | x | square root of x squared end root , equals absolute value of x ,  for all real numbers x.

Example

Simplify each expression.

1. 50     50 = 25 ⋅ 2 Multiplication Property of Square Roots   = 5 2 Simplify . table with 3 rows and 3 columns , row1 column 1 , square root of 50 , column 2 , column 3 , row2 column 1 , square root of 50 , column 2 equals square root of 25 dot square root of 2 , column 3 cap multiplicationcap propertyofcap squarecap roots , row3 column 1 , , column 2 equals 5 square root of 2 , column 3 cap simplify , . , end table
2. 5 11     5 11 = 5 11 Division Property of Square Roots   = 5 11 ⋅ 11 11 Multiply both the numerator and denominator by  11 .   = 55 121 Multiplication Property of Square Roots .   = 55 11 Simplify . table with 5 rows and 3 columns , row1 column 1 , square root of 5 elevenths end root , column 2 , column 3 , row2 column 1 , square root of 5 elevenths end root , column 2 equals , fraction square root of 5 , over square root of 11 end fraction , column 3 cap divisioncap propertyofcap squarecap roots , row3 column 1 , , column 2 equals , fraction square root of 5 , over square root of 11 end fraction , dot , fraction square root of 11 , over square root of 11 end fraction , column 3 cap multiplyboththenumeratoranddenominatorby . square root of 11 . , row4 column 1 , , column 2 equals . fraction square root of 55 , over square root of 121 end fraction , column 3 cap multiplicationcap propertyofcap squarecap roots . . , row5 column 1 , , column 2 equals , fraction square root of 55 , over 11 end fraction , column 3 cap simplify , . , end table

Exercises

Simplify each radical expression.

1. 18 square root of 18
2. 75 square root of 75
3. − 32 negative square root of 32
4. − 5 7 square root of negative 5 over 7 end root
5. − 7 13 negative , square root of 7 thirteenths end root
6. 3 15 square root of 3 fifteenths end root
7. − 200 negative , square root of 200
8. 5 320 5 , square root of 320
9. ( 2 27 ) 2 open , 2 square root of 27 , close squared
10. − 10 4 negative , square root of 10 to the fourth end root
11. x 2 y 2 square root of x squared , y squared end root
12. 8 x 2 square root of fraction 8 , over x squared end fraction end root
13. − 7 x 3 5 x negative . square root of fraction 7 , x cubed , over 5 x end fraction end root
14. ( − 3 ) 4 12 square root of fraction open , negative 3 , close to the fourth , over 12 end fraction end root
15. 200 28 square root of 200 over 28 end root
16. 120 x square root of 120 x end root

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