Question

I have a square root that is y to the third how do i simplify it?

Answer 1

Fill in the blank \(\Large y^3=y^2 *\underline{ \ \ \ \ \ }\)

Answer 2

y

Answer 3

good

Answer 4

so

\[\Large \sqrt{y^3} = \sqrt{y^2*y}\]

Answer 5

we would then break up that root to get

\[\Large \sqrt{y^3} = \sqrt{y^2*y}\]

\[\Large \sqrt{y^3} = \sqrt{y^2}*\sqrt{y}\]

\[\Large \sqrt{y^3} = y*\sqrt{y} \ ... \ \text{assuming } y \ge 0\]

Answer 6

so the key here is to factor the expression into pieces that have squares

that way, when you break it up, you can take the square root of those squares to make them go away

Answer 7

Ok I think ive got it, THANKS!

Answer 8

Another example

\[\Large \sqrt{z^5} = \sqrt{z^2*z^2*z}\]

\[\Large \sqrt{z^5} = \sqrt{z^2}*\sqrt{z^2}*\sqrt{z}\]

\[\Large \sqrt{z^5} = z*z*\sqrt{z} \ ... \ \text{assuming } z \ge 0\]

\[\Large \sqrt{z^5} = z^2*\sqrt{z} \ ... \ \text{assuming } z \ge 0\]

Answer 9

you're welcome

Answer 10

One piece of advice: What you had to work with is a "cube root," not a square root. You could also speak in terms of "third root."