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Pearson Algebra 2 Common Core, 2011

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Pearson Algebra 2 Common Core, 2011 View details

End-of-Course Assessment

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Exercise 52 Page 969

If n is an odd number, then the radical expression sqrt(a^n) simplifies to a. If n is even, the expression sqrt(a^n) simplifies to |a|.

4y^6|x|

Practice makes perfect

For any real number a, the radical expression sqrt(a^n) can be simplified as follows. sqrt(a^n)= a if n is odd |a| if n is evenBecause the given root has an even index and the variables have even exponents, we will use the absolute value symbol to simplify the expression.

sqrt(16x^2y^(12))

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

sqrt(16) * sqrt(x^2 y^(12))

Calculate root

4 sqrt(x^2 y^(12))

Rewrite 12 as 6* 2

4sqrt(x^2y^(6* 2))

a^(m* n)=(a^m)^n

4sqrt(x^2(y^6)^2)

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

4sqrt(x^2) * sqrt((y^6)^2)

sqrt(a^2)=|a|

4|x| * |y^6|

Since y is raised to an even power, y^6 is positive. Therefore, |y^6| = y^6. Let's simplify our expression further. 4|x| * |y^6| = 4y^6|x| This is the simplest form of the given expression.

Subchapter links

Exercises p.964-971