radicals..?

Question

k imagine a square root sign..
and inside of it..
28x^9y^6
now simplify?

Answer 1

sqrt (28 x^9 y^6)

Break off an x to make sure the powers are even. Also, note that 28 = 4 x 7

sqrt ( (4)(7)x x^8 y^6 )

Now, we remove the 4, x^8 and y^6 out of the square root. The moment they are pulled out of the square root, you take the square root of them. The 4 pulled out of the square root becomes 2, the x^8 becomes x^4, and the y^6 becomes y^3.

2(x^4)(y^3) sqrt (7x)

That should be your final answer.

Answer 2

Square root of (28x^9y^6)

I would simplify into perfect squares first:

Square root of (7*4*x^8*x*y^6)

Take the square root of the perfect squares, and leave everything else inside the square root sign:

2x^4y^3 * Square root of (7x)

Answer 3

doesn't get much simpler than that.
weird homework question?

is it 28x^(9y^6)
or (28x^9y)^6
?

do you know: you can think of the square root as an (1/2) exponent.

so sqrt(x^6) = (x^6)^(1/2) = x^(6/2) = x^3

Answer 4

√[28*x^9*y^6] = √28 * √x^9 * √y^6 = 2√7 * √x*√x^8 * y^3 = (2√7) * (x^4)*√x * (y^3)