Question

Simplify this square root
Square root 144x^9y^7
I think the next step is to take the square root of 144, so
12(x^9y^7)^1/2. What is next?

Answer 1

divide 9 into 2 to get

9/2 = \(\Large {\color{red}{4}}\) remainder \(\Large {\color{blue}{1}}\)

the \(\Large {\color{red}{4}}\) will be the exponent for the x outside the square root
the \(\Large {\color{blue}{1}}\) will be the exponent for the x inside the square root

so
\[\Large \sqrt{x^9} = x^{{\color{red}{4}}}\sqrt{x^{{\color{blue}{1}}}} = x^4\sqrt{x}\]

Answer 2

Another example. Let's say we had the square root of x^17

Divide 17 in half to get

17/2 = \(\Large {\color{red}{8}}\) remainder \(\Large {\color{blue}{1}}\)


Which means

\[\Large \sqrt{x^{17}} = x^{{\color{red}{8}}}\sqrt{x^{{\color{blue}{1}}}} = x^8\sqrt{x}\]

Answer 3

I wish I could write like that. So, would my answer be
12x^4 ( sq rt x) x^3 (sq rt x)
12 x^7 times x
12x^8
?

Answer 4

You forgot about y. There aren't two x terms

Answer 5

But yes,
\[\Large \sqrt{y^7} = y^3\sqrt{y}\]

Answer 6

Duh, let me try again

Answer 7

btw you can use the equation editor (the blue "equation" button below the text box)

Answer 8

or you can type it in by hand like so

type in `\(\Large \sqrt{x}\)` to get \(\Large \sqrt{x}\)

Answer 9

12x^4(sq rt x)y^3(sq rt y)

Answer 10

from there you can combine the stuff in the roots using this rule

\[\Large \sqrt{x*y} = \sqrt{x}*\sqrt{y}\]

Answer 11

I'm using an iPad and don't see the equation editor?

Answer 12

hmm I'm not sure how the layout is for the iPad. I guess you'll have to type it in by hand if you want the equations to render like that

Answer 13

Anyways, using that rule, you'll go from this
\[\Large 12x^4\sqrt{x}*y^3\sqrt{y}\]
to this
\[\Large 12x^4y^3\sqrt{xy}\]

Answer 14

So
\[\Large \sqrt{144x^9y^7}\]
fully simplifies to
\[\Large 12x^4y^3\sqrt{xy}\]

Answer 15

I really appreciate your help!

Answer 16

glad to be of help