Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
2. Simplifying Radicals
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Exercise 63 Page 624

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

xsqrt(y)/y^2

Practice makes perfect

We want to simplify a radical expression. To do so we will assume that y>0, otherwise the given expression would not be defined. sqrt(x^2)/sqrt(y^3) Let's recall the Multiplication Property of Square Roots. sqrt(ab)=sqrt(a) * sqrt(b), for a≥ 0,b≥ 0 Let's use this property for our expression.

sqrt(x^2)/sqrt(y^3)
sqrt(x^2)/sqrt(y^2* y)
sqrt(x^2)/sqrt(y^2)sqrt(y)
x/ysqrt(y)

Now that we have simplified the factors as much as possible, we need to rationalize the denominator. To do this, we will multiply the numerator and denominator by a square root that will eliminate the radical in the denominator.

x/ysqrt(y)
xsqrt(y)/ysqrt(y)* sqrt(y)
xsqrt(y)/y* y
xsqrt(y)/y^2