Name DateWORKSHEET 7.8: SIMPLIFYING SQUARE ROOTS
OF NEGATIVE NUMBERS
-------------------------------------------------------------------------------------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.
267Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.