Simplify Each Radical:
Introduction to Simplifying Radicals
Simplify Each Radical:
1) √48 2) √128 3) √363 4) √45
5) √25x2 6) √72x8 7) √432x16y8 8) √392x100y210
9) √x9 10) √x9y10 11) √x9y11 12) √25x9y11
13) √162x10y5 14) √75x7y3 15) √300x5y12 16) √169x100y64
17) √108x16y25 18) √98x1000y500 19) √600x11y14 20) √-36
Imaginary Numbers
You can’t take the square root of -36 (or of any other negative number). Think about it.
36 = ± 6, because 6 · 6 = 36 and -6 · -6 = 36. But you cannot multiply a number by itself and get a negative number. We use the imaginary unit i to write the square root of any negative number.
√-1 = i
√-36 ( √36 · -1 ( 6i
Simplify Each Radical:
1) √-8 2) √-50 3) 4√-242 4) 7√-125
5) 2√-384 6) √-245 7) √-588 8) √-361
Simplifying with i:
i1 = i5 = i9 = i13 = i33 =
i2 = i6 = i10 = i14 = i38 =
i3 = i7 = i11 = i15 = i43 =
i4 = i8 = i12 = i16 = i44 =
When simplifying and using operations with imaginary numbers, you are not allowed to leave i with an exponent. How possible terms can you have when you simplify?
We have a simple way of remembering how to simplify:
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1) i1 2) i2 3) i3 4) i4
5) i5 6) i6 7) i7 8) i8
9) i9 10) i10 11) i11 12) i12
13) i21 14) i33 15) i32 16) i26
17) (√-10)2 18) √-10 · √-20 19) √-3 · √-12 20) √-18 · √-6
21) (3i)2 22) (i√3 )2 23) (-i )2 24) – i2
25) (9i5)(-6i13) 26) (-8i7)(-13i17) 27) (-5i11)(12i10) 28) (-11i23)(-12i16)
Complex Numbers
A complex number is a number that is the sum of a real number and a regular number. Each complex number should be written in the standard form a + bi. Example: 8 + 3i
Perform the indicated operation:
29) (11- 5i)(7 – 3i) 30) (4 + 5i)(7 – 3i) 31) 2i2(3 – 8i) – 4i(12 – 7i)
32) (9 + 3i)(12 + 2i) 33) 5i2(3 + 2i) – 3i2(4 + 8i) 34) (4 + 2i) + (7 – 2i)
35) 3(6-2i) – 4(4 + 3i) 36) 8i(9 + 2i) – 3i(3 - 7i) 37) (3 – 2i)(4 + 5i)
Practice Problems: #1 can be done on the sheet, the rest should be done in your NB.
1) Simplify:
i21 = i58 = i92 = i123 = i45 =
i26 = i61 = i19 = i129 = i58 =
i35 = i72 = i14 = i106 = i74 =
i48 = i87 = i66 = i116 = i1,000 =
2) √-108 3) √-486 4) 8√-392 5) -7√-675 6) 9√-441
7) 12(5 – 7i) + 10(-6 + 8i) 8) 3i(4 – 10i) – 7(8 + 5i)
9) 6(3 + 2i) + 8i(4 + 9i) 10) 9i(4 – 11i) – 6i2(-10 – 4i)
11) (3 – 2i)(4 + 5i) 12) (10- 4i)(6 – 2i)
13) (9 + i)(8 – 5i) 14) (6 + 7i)(6 + 2i)
15) (5 – 8i)(11 + 9i) 16) (10- 3i)(7 – 12i)
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