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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
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.
Split into factors
sqrt(a* b)=sqrt(a)*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.
Commutative Property of Multiplication
Write as a product of fractions
a/a=1
Identity Property of Multiplication
a/b=a * sqrt(3)/b * sqrt(3)
sqrt(a)*sqrt(b)=sqrt(a* b)
sqrt(a)* sqrt(a)= a
Calculate quotient