Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
Mid-Chapter Quiz
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Exercise 15 Page 632

The Multiplication Property of Square Roots tells us that sqrt(ab)=sqrt(a) * sqrt(b), for a≥ 0 and b≥ 0.

- 12bsqrt(b)

Practice makes perfect
We want to simplify a radical expression. To do so we will assume that b ≥ 0, otherwise the given expression would not be defined. - 2sqrt(3b^2) * sqrt(12b) Let's recall the Multiplication Property of Square Roots. sqrt(ab)=sqrt(a) * sqrt(b), for a≥ 0,b≥ 0 We can use this property for our expression.
- 2sqrt(3b^2) * sqrt(12b)
- 2sqrt(3* b^2) * sqrt(4* 3 * b)
- 2sqrt(3)sqrt(b^2) * sqrt(4)sqrt(3)sqrt(b)
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Simplify Factors
- 2sqrt(3)sqrt(b^2) * 2sqrt(3)sqrt(b)
- 2sqrt(3) b * 2sqrt(3)sqrt(b)
Now that we have simplified the factors as much as possible, we can use the Commutative Property of Multiplication to simplify even further.
- 2sqrt(3) b * 2sqrt(3)sqrt(b)
-2(2)sqrt(3) sqrt(3)b sqrt(b)
-2(2)3b sqrt(b)

Multiply

- 12bsqrt(b)