Created by K.Snyder 1

H-A2-TRIG UNIT 3

SIMPLIFYING RADICALS (DAY 1)

List the following PERFECT…

Squares Cubes (3rd roots) 4th roots

12 = 13 = 14 =

22 = 23 = 24 =

32 = 33 = 34 =

42 = 43 = 44 =

52 = 53 = 54 =

62 = 63 = 64 =

72 =

82 =

92 =

102 =

Radicals with Variables: For a variable to be “perfect” the exponent on the variable must

be divisible by the _______________.

For a square root, the variable’s exponent must be divisible by ______.

For a cube root the variable’s exponent must be divisible by ______.

For a fourth root the variable’s exponent must be divisible by ______.

If the variable’s exponent is not divisible by the index, break up the exponent into the next

lower number that is divisible by the index.

1) 8x 2) 11x 3) 3 15x

4) 3 29x 5) 4 187yx

Index

(nth root)

Radical sign

Radicand

d

n x

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Radicals with Numbers and Variables: Simplify the numbers using the appropriate list of

“perfect” numbers, and simplify the variables.

6) 5x28 7) 3 8y54 8) 4 195yx486

Radicals with Negative Radicands must be ODD root:

Pull out the negative with the “perfect” root number.

9) 3 13x402 10) 3 176ba162

1

Radicals with Fractional Radicands: Distribute the radical sign to the numerator and to the

denominator and simplify each.

11) 25

x9 6

12) 3

106

64

yx48 13) 5 5x

1024

1

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SIMPLIFYING RADICALS (DAY 1b) Radicals with Irrational Denominators:

Divide #’s under radical if possible

Separate Top # and Bottom # under their own Radical

Irrational Denominator needs to be made Rational by….

o MULTIPLYING top and bottom by the irrational denominator

1) v20

9 2)

x6

2

Simplify the following radicals.

3) 7x98 4)

3 164

5)

4 132yx322

1

6) 8

11

b121

a9

7) 3 29x545 8) 4x4x2

9) 3 162yx250

10) 25147 zyx1474

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ADDING AND SUBTRACTING RADICALS (DAY 2) Procedure:

Write each expression in simplest form.

1) 50722 2) 1227

3) 99 x215x18 4) yx50y72x 27

5) 3

1452012 6) x300

x3

1x3

7) 33 54516 8) 44 2162

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9) 99 b800b32 10) cba1922

1cba75

5

3 6464

11) The sides of a triangle measure 3 243 , 3 27 and 3 812 . The perimeter of this triangle is

(1) 33123 (2) 333 (3) 336 3 (4) 3 312

12) Solve for x: 4x - 8 = 72

13) In the equation 300 - 5x = 75 , the value of x is

(1) 35 (2) 35 (3) 3 (4) 15

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MULTIPLYING RADICALS (DAY 3) Procedure:

Express the following in simplest form.

1) 105 2) 2385 3) 33 278

4) 4

24 2

3

xx48 5) 1223 6) a21a63

7) 33432 8) 7575 9) 4 24 2 b4a2b4a

**Remember: nnn because 2)n(nn = n

A square & a square root are opposite operations and cancel each other leaving n

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10) The length of a side, s, of an equilateral triangle is 5 inches and the length of the

altitude, h, is 4

15 inches . Find the area of the triangle.

11) The length of a rectangle is represented by the expression 6 + 122 . The width of the

rectangle is represented by 3 + 34 . Which expression represents the area of the

rectangle?

(1) 66 + 36 3 (2) 9 + 38 (3) 18 + 316 (4) 32 + 363

12) Which example produces a product of 18?

(1) 62563 (3) 324324

(2) 2523 (4) 236236

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DIVIDING RADICALS (DAY 4) Procedure:

Write each quotient in simplest form.

1) 5812516 2) 3

75150

3) xy8

yx360 53

4) 63

24304815

5) 3 2

3 29

x10

x80

6) Express 3a3a27 in simplest radical form when a is a positive real number.

7) The area of a rectangle is 25yx2428 , and it has a base of yx67 3 . Find the height of

the rectangle in simplest radical form.

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RATIONALIZING DENOMINATORS (DAY 5)

When the denominator of a fraction contains a radical, we must rationalize the fraction to

get a real, rational number.

Procedure for Rationalizing with Monomial Denominators:

Express the following in simplest radical form.

1) 3

6 2)

52

5 3)

106

1

Conjugates:

Write the conjugates of the following binomials.

1) 2 - 5 2) 6 - 4 3) 2 + 7

For each problem above, multiply the original binomial and the conjugate together.

1) 2) 3)

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Procedure for Rationalizing with Binomial Denominators:

Express the following in simplest radical form.

1) 32

7

2)

31

2

3) 71

3

4)

22

2

5) 23

21

6)

35

32

7) 53

51

8)

71

71

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RADICAL EQUATIONS (DAY 6)

Procedure for Solving Radical Equations:

1) 42x6 2) 4x85

3) x3x5 4) 2a243

5) 623x22 6) x15x