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# √448x∧8y∧19

### 2 Answers by Expert Tutors

Kathye P. | Math Geek, passionate about teachingMath Geek, passionate about teaching
5.0 5.0 (150 lesson ratings) (150)
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Hi, Mondrea.

to simplify a radical, we break it up into perfect squares. For variables, even exponents are perfect squares.

448 = 64 * 7
x8 is a square
y19 = y18 * y

So, we have √64 * √7 * √x8 * √y18 * √y
= 8 * √7 * x4 * y9 * √y
= 8x4y9√7y

Hope that helps!
Kathye P.

BTW, on large numbers, you can also break them down a little at a time, if that helps.
For example, 448 = 4 * 4 * 4 * 7

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
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Simplify √(448 x^8 y^19)

Find perfect square factors:

448 = 4*112 = 4*4*28 = 4*4*4*7
= (4^2)*(2^2)*7 = (8^2)*7

x^8 = (x^4)^2

y^19 = y*(y^18) = y*(y^9)^2

√(448 x^8 y^19)

= √( (8^2)*7*(x^4)^2*y*(y^9)^2 )

= √( (8^2)*(x^4)^2*(y^9)^2*7*y )

= 8*(x^4)*(|y|^9)*√(7 y)

The absolute value on y^9 is because √((y^9)^2) is always positive so it's simplified version must be positive too.