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 18 Page 632

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

sqrt(6)x

Practice makes perfect

We want to simplify a radical expression. To do so we will assume that x>0, otherwise the given expression would not be defined. - 3sqrt(14x^3)/- sqrt(21x) Let's recall the Multiplication Property of Square Roots and the Division Property of Square Roots. sqrt(ab)=sqrt(a) * sqrt(b), for a≥ 0,b≥ 0 sqrt(ab)= sqrt(a)sqrt(b),for a≥ 0,b>0 We can use these properties for our expression.

- 3sqrt(14x^3)/- sqrt(21x)
- 3sqrt(2* 7* x* x^2)/- sqrt(3* 7* x)
- 3sqrt(2)sqrt(7* x)sqrt(x^2)/- sqrt(3)sqrt(7* x)
â–¼
Simplify
- 3sqrt(2)sqrt(7* x)x/- sqrt(3)sqrt(7* x)
3sqrt(2)sqrt(7* x)x/sqrt(3)sqrt(7* x)

Now that we have simplified the factors as much as possible, we can use the Commutative Property of Multiplication to simplify even further.

3sqrt(2)sqrt(7* x)x/sqrt(3)sqrt(7* x)
3sqrt(2)x* sqrt(7* x)/sqrt(3)* sqrt(7* x)
3sqrt(2)x/sqrt(3)* sqrt(7* x)/sqrt(7* x)
3sqrt(2)x/sqrt(3)* 1
3sqrt(2)x/sqrt(3)
3sqrt(2)* sqrt(3)x/sqrt(3)* sqrt(3)
3sqrt(6)x/sqrt(3)* sqrt(3)
3sqrt(6)x/3
sqrt(6)x