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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