Question

Can someone help me with this one problem?(: will fan and medal
sqrt 50x^7y^7 * sqrt 6xy^4

Answer 1

\[\large \sqrt{50x^7y^7} \times \sqrt{6xy^4}\]

Like that?

Answer 2

yes!:)

Answer 3

Alright, well a couple ways to do this..but to make sure there's no giant number to deal with...lets start off with a quick simpification

\[\large \sqrt{50x^7y^7} \times \sqrt{6xy^4}\]
Can be written as
\[\large \sqrt{(25\times 2) x^7y^7} \times \sqrt{6xy^4}\]

All I changed was 50 is now expressed as 25 times 2

Answer 4

So now...with that 25...we can look at everything separate so we can just focus on the

\[\large \sqrt{25}\]

Notice anything? can that be simplified?

Answer 5

yeah

Answer 6

5

Answer 7

Great! And okay...so back to the whole original question

\[\large \sqrt{(25\times 2)x^7y^7} \times \sqrt{6xy^4}\]

Now that we know the square root of 25 is 5...we can take the '5' out of the square root

\[\large 5\sqrt{2x^7y^7} \times \sqrt{6xy^4}\]

That make sense?

Answer 8

yeah!

Answer 9

Okay cool...

Next step, remember that when you multiply square roots...everything under both square roots is now under 1 and being multiplied.

Example \(\large \sqrt{2}\times \sqrt{3} = \sqrt{2\times 3}\) okay?

Answer 10

okay

Answer 11

Soooo with your question here...we have

\[\large 5\sqrt{2x^7y^7} \times \sqrt{6xy^4}\]

And when we multiply everything...we have

\[\large 5\sqrt{2x^7y^7\times 6xy^4}\]

just combined em under the radical

Answer 12

So now...we just need to multiply everything together...

what is \(\large 2x^7y^7 \times 6xy^4\) ?

Answer 13

i got 12x^8y^11

Answer 14

Perfect :) Okay...now remember all that is under the radical...so we have

\[\large 5\sqrt{12x^8y^{11}}\]

Remember how I broke up 50 into 25 times 2 because the 25 has an easy square root?

can 12 be broken up in the same way?

Answer 15

yeah

Answer 16

And how can that be broken up?

Answer 17

3 and 4

Answer 18

wait..i dont know D:

Answer 19

No no you got it :DD

Answer 20

oh okay!

Answer 21

Because 4 has an easy square root of 2 :D

Answer 22

So we have

\[\large 5\sqrt{(4\times 3)x^8y^{11}}\]

which we can then write as

\[\large (5\times 2)\sqrt{3x^8y^{11}}\]

When we take the 2 out of the square root...it then gets multiplied to that 5 we already had out there...so obviously 5 times 2 is 10 so

\[\large 10\sqrt{3x^8y^{11}}\]

Answer 23

Still with me? :)

Answer 24

yeah!:)

Answer 25

Great!...

Alright...now is where it gets...odd? We can only continue simplifying if we assume that 'x' and 'y' are positive..

But as of now...this is the final simplification.

Answer 26

IF,and that is only depending on your assignment,we do assume that 'x' and 'y' are positive...then we can just do the last step...so you let me know if you would like to see this part...or if it's not needed :)

Answer 27

well, it's not really needed but I would still like to see it to get the idea:)

Answer 28

Okay :)

So, assuming that 'x' and 'y' are positive...we have

\[\large 10\sqrt{3x^8y^{11}}\]

Sidebar: How else can we write \(\large \sqrt{x}\) ? More specifically...in terms of exponents!

Answer 29

erm, im not sure

Answer 30

\[\Large \sqrt{x} = x^{\frac{1}{2}}\]

Answer 31

You can definitely read more about this because it DOES come in handy

But for now..take my word for it :D

Okay...back to your problem

\[\large 10\sqrt{3x^8y^{11}}\]

We can write that as

\[\Large 10(3x^8y^{11})^\frac{1}{2}\]

Answer 32

What happens when we have an exponent on the outside of a parenthesis...what do we do?

\[\large (x^2)^3\]

What is that?

Answer 33

would it be x^6

Answer 34

Sorry hun I have to head out for a bit...so I'm gonna do a quick summary

So to answer that last thing...we multiply instead of add like normal..

\[\large (x^2)^3 = x^6\]

Knowing that...when we look at your question..

\[\large 10(3x^8y^{11})^{\frac{1}{2}}\]

We can raise everything in the parenthesis to that one-half power...so

\[\large 10(3^{1/2})(x^8)^{1/2}(y^{11})^{1/2}\]

What is 3 to the 1/2 power? well it is just the same...3 to the 1/2 power...or (as we now know...is the square root of 3...so we have

\[\large 10\sqrt{3}(x^8)^{1/2}(y^{11})^{1/2}\]

What is \(\large (x^8)^{1/2}\) ?? we just learned we multiply the 8 and the 1/2 so we have

\[\large 10\sqrt{3}x^{4}(y^{11})^{1/2}\]


Now finally we just multiply the 11 times the 1/2 and we get

\[\large 10\sqrt{3}x^4y^{11/2}\]

Which is TRUELY the final simplification!

If you still need help on this...feel free to tag another helper...or tag me back and I'll take a look when I return :)

Answer 35

Well thank you so much for your help! I really appreciate it:)

Answer 36

Of course! Anytime :)