Question

Find the exact value of the radical expression in simplest form.
the square root of 16 times y cubed − the square root of y cubed

3 times y times the square root of y

3 times y squared times the square root of y

4 times y squared times the square root of y

4 times y times the square root of y

Answer 1

\[\sqrt{16y^3} - \sqrt{y^3}\]

Answer 2

\[\Large \sqrt { 16 y^3} - \sqrt {y^3}\]
Break up the square roots like last time \[\Large \sqrt { 16} \sqrt{y^3} - \sqrt {y^3}\]

Answer 3

4 sqrt y^3-y^3

Answer 4

now what do you do?

Answer 5

Now break the y^3 up into y^2*y... \[\large y^3 = y^2 \times y\] understand why?

\[\Large \sqrt { 16} \sqrt{y^3} - \sqrt {y^3} = \] \[\Large 4 \sqrt{y^2 \times y} - \sqrt {y^2 \times y} = \]

Answer 6

yes, and when you do that you get \[4y \sqrt{y}\] ?

Answer 7

I think you missed a term, check again - you're partially correct :)

Answer 8

oh I got it now! \[4y^2\sqrt{y}\]

Answer 9

Hmm, not quite. Do it one step at a time, simplify the left term and the right term \[\Large 4 \sqrt{y^2 \times y} - \sqrt {y^2 \times y} =\]
\[\Large 4 y \sqrt{ y} - y\sqrt { y} =\]

Answer 10

3y sqrt y

Answer 11

Excellent :)

Answer 12

haha, thank you :)

Answer 13

Welcome :)