Question

Help with dividing radical expressions?? I don't understand it at all!

Answer 1

\[\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\]

Answer 2

\[\sqrt[3]{-243x^3y^{10}}\]

Answer 3

Simplifying** sorry..

Answer 4

Think of the perfect cubes:
\[2^3=8\]
\[3^3=27\]
\[4^3=27\]

Answer 5

4^3=64

Answer 6

Is 343 a perfect cube or does it contain a perfect cube factor?

Answer 7

Contains.?

Answer 8

Yes. 243 = 27 x 9

Answer 9

So - 243 = -27 x 9
Also rewrite the variable so that the exponents are multiples of 3

Answer 10

x^3 is already in the right form but y^10 should be written y^9 x y

Answer 11

So now we have:
\[\sqrt[3]{-27(9)x^3y^9y}\]

Answer 12

So finish it up by taking the 3rd root of -27, x^3, y^9