Pearson Algebra 1 Common Core, 2011
PA
Pearson Algebra 1 Common Core, 2011 View details
1. Simplifying Rational Expressions
Continue to next subchapter

Exercise 64 Page 669

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

sqrt(2)/5 m^2

Practice makes perfect

We want to simplify a radical expression. To do so we will assume that m>0, otherwise the given expression would not be defined. sqrt(2m/25m^5)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 Now let's simplify the fraction and then we will use the above properties.

sqrt(2m/25m^5)
sqrt(2m/25m^(1+4))
sqrt(2m/25 m * m^4)
sqrt(2m/25 m * m^4)
sqrt(2/25 * m^4)
sqrt(2)/sqrt(25 * m^4)
sqrt(2)/sqrt(25) * sqrt(m^4)
â–¼
Simplify Factors
sqrt(2)/5 * sqrt(m^4)
sqrt(2)/5 * sqrt(m^(2 * 2))
sqrt(2)/5 * sqrt((m^2)^2)
sqrt(2)/5 m^2