## express in simplified form

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# 2 Answers

Hi, Mondrea.

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

448 = 64 * 7

x

^{8}is a squarey

^{19}= y^{18}* ySo, we have √64 * √7 * √x

^{8}* √y^{18}* √y= 8 * √7 * x

^{4}* y^{9}* √y= 8x

^{4}y^{9}√7yHope 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

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.

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