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) √288x36y144
Simplify Each Radical:
1) √49x49y81 2) √72x8 3) √363x16y8 4) √392x100y210
5) √450x10y5 6) √75x7y3 7) √300x5y12 8) √-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:
9) √-8 10) √-50 11) √-242 12) √-125
13) √-384 14) √-245 15) √-588 16) √-361
17) i1 18) i2 19) i3 20) i4
21) i5 22) i6 23) i7 24) i8
25) i9 26) i10 27) i11 28) i12
29) i21 30) i33 31) i32 32) i26
33) (√-10)2 34) √-10 · √-20 35) √-3 · √-12 36) √-18 · √-6
37) (3i)2 38) (i√3 )2 39) (-i )2 40) – i2
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:
33) (4 + 2i) + (7 – 2i) 34) 3(6-2i) – 4(4 + 3i) 35) 5i(3 + 2i) – 3i(4 + 8i)
36) (3 – 2i)(4 + 5i) 37) (11- 5i)(7 – 3i) 38) (4 + 5i)(7 – 3i)
39) 2i2(3 – 8i) – 4i(12 – 7i) 40) (9 + 3i)(12 + 2i) 41) 5i2(3 + 2i) – 3i2(4 + 8i)
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