Question

sq rt (4x^2) * sq rt (28x)

Answer 1

\[\sqrt {4x^2} * \sqrt {28x}\]look at the 4x^2 term first. What can that be simplified to?

Answer 2

4x because the square root and the power cancel

Answer 3

There is a property where \[\large (ab)^x=a^xb^x\]So the 1/2 power has to be applied to each term under the radical

Answer 4

half?

Answer 5

\[\huge \sqrt x=x^{1/2}\]

Answer 6

that is what the radical means

Answer 7

\[\large \sqrt {4x^2}=(4x^2)^{1/2}=4^{1/2}x^{2*1/2}\]

Answer 8

\[\sqrt{4x^2}=\sqrt{4}\times \sqrt{x^2}=2x\]

Answer 9

2x*28x

Answer 10

28x is still under the radical tho. We haven't simplified that part yet

Answer 11

Now sqrt(x) can't be simplified but we can do something for sqrt(28) we can split it up into its factors, one being a perfect square so that we can simplify it. \[\sqrt{28}=\sqrt{4*7}=\sqrt4\sqrt7=2\sqrt7\]

Answer 12

\[\large 2x*2\sqrt{7x}=4x \sqrt{7x}=4x^{3/2}\sqrt7\]

Answer 13

where did the 3/2 come from?

Answer 14

\[\huge x^ax^b=x^{a+b}\]