Exercise 63 Page 669

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

3xsqrt(11)

Practice makes perfect

We want to simplify a radical expression. sqrt(9x) * sqrt(11x) 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. To do this we need to assume that x is greater than or equal to 0.

sqrt(9x) * sqrt(11x)

SplitIntoFactors

Split into factors

sqrt(9 * x) * sqrt(11 * x)

SqrtProd

sqrt(a* b)=sqrt(a)*sqrt(b)

sqrt(9) * sqrt(x) * sqrt(11) * sqrt(x)

CalcRoot

Calculate root

3* sqrt(x) * sqrt(11) * sqrt(x)

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

3* sqrt(x) * sqrt(11) * sqrt(x)