Exercise 25 Page 265

To simplify the given expression, we can first rewrite the radical as a quotient of two radicals. sqrt(50/a^2)=sqrt(50)/sqrt(a^2)While simplifying, we should consider the index of the radical in the denominator to see how we should format our solution. sqrt(a^n)= a if n is odd |a| if n is even Because the radical in the denominator has an even root and the variable has an even exponent, we will need to use absolute value symbols to simplify our expression.

sqrt(50)/sqrt(a^2)

SqrtToAbs

sqrt(a^2)=|a|

sqrt(50)/|a|

SplitIntoFactors

Split into factors

sqrt(2*25)/|a|

ProdSqrt

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

sqrt(2)*sqrt(25)/|a|

CalcRoot

Calculate root

sqrt(2)*5/|a|

CommutativePropMult

Commutative Property of Multiplication

5sqrt(2)/|a|