H-A2-TRIG UNIT 3 SIMPLIFYING RADICALS (DAY 1)€¦ · 1 Created by K.Snyder H-A2-TRIG UNIT 3...
Transcript of H-A2-TRIG UNIT 3 SIMPLIFYING RADICALS (DAY 1)€¦ · 1 Created by K.Snyder H-A2-TRIG UNIT 3...
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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