Name Date
WORKSHEET 7.2: MULTIPLYING RADICALS
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Multiplying radicals requires the use of the product property of square roots that states the
square root of a product equals the product of the square root of the factors.√xy=
√
x·√y,
wherexandyare real numbers that are greater than or equal to 0. Follow the steps below:
- Multiply the radicands.
- Simplify the radicals.
- Multiply the coefficients.
EXAMPLE
4
√
3 ·
√
6
4
√
3 ·
√
6 = 4
√
18
4
√
18 can be simplified as 4
√
9 ·
√
2.
4 · 3
√
2 = 12
√
2
DIRECTIONS: Simplify each expression.
√
4 ·
√
5 2.
√
7 ·
√
8 3. 3
√
6 · 2
√
3
√
15 ·
√
3 5. 2
√
5 ·
√
7 6. 3
√
3 ·
√
18
- − 4
√
3 ·
√
5 8. − 5
√
10 ·
√
8 9. − 3
√
10 · 4
√
15
- 6
√
8 ·
√
2 11. 3
√
10 ·
√
3 12. 8
√
2 ·− 2
√
2
CHALLENGE:Bobby said that he found a faster way to multiply radicals by
simplifying a radical before he multiplied. For example, when Bobby was
solving the problem
√
8 ·
√
6, he first expressed
√
8as2
√
2andthen
multiplied 2
√
2and
√
6, which equals 2
√
- Do you agree with his method?
Will it always work? Explain.
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Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.