Name Date
WORKSHEET 7.8: SIMPLIFYING SQUARE ROOTS
OF NEGATIVE NUMBERS
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The square root of a negative number can be simplified by using the imaginary uniti,whichis
equal to
√
− 1. Follow the steps below to simplify the square roots of negative numbers:
- Factor the radicand by finding the product of
√
− 1 and the other radicand.
- Replace
√
− 1 byi.
- Simplify the radical.
- Multiply the numbers directly preceding the radicals, if applicable.
EXAMPLE
Simplify 7
√
− 48.
7
√
− 48 = 7
√
− 1 ·
√
48 = 7 i
√
48 = 7 i
√
16 ·
√
3 = 7 i· 4
√
3 = 28 i
√
3
DIRECTIONS: Simplify each expression.
√
− 16 2. 4
√
− 20
√
− 27 4.
√
− 12
- 2
√
− 30 6. 3
√
− 18
√
− 10 8. 4
√
− 54
- 3
√
− 24 10. − 4
√
− 50
CHALLENGE:Marta expressed
√
−512 in simplified form as 8i
√
- Was she
correct? Explain your answer.
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Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.