Question

square root of 320a cubed, b to the fifth power

Answer 1

\[\sqrt{320a ^{3} b ^{5}}\]

Answer 2

Since none of these are perfect squares, we'll have to start by factoring.
\[\sqrt{320a^3 b^5} = \sqrt{16 \times 4 \times 5 \times a^2 \times a \times b^4 \times b}\] All I did there was split up 320 into three of its nicest factors, and split up the varibles into some better numbers.
We suddenly have two perfect squares we can pull out!
\[\sqrt{16} = 4\] and \[\sqrt{4} = 2\] So let's put those on the outside of the radical.\[8\sqrt{5a^2 \times a \times b^4 \times b}\] From here, let's go ahead and pull out some variables.\[\sqrt{a^2} = a\] so we'll take that one out from under the radical.\[\sqrt{b^4}= b^2\] And we'll take that out too.

Let's look at what we have now:\[8ab^2\sqrt{5ab}\] Looks like we have no more factors we can pull out, so we're done!

Answer 3

thanks!! i got another problem i cannot figure out

Answer 4

\[(7\sqrt[3]{49})(7\sqrt[3]{7})\]

Answer 5

That one's a little different because you're multiplying two radicals with the same index (the little 3 is the index) together. It's pretty straightforward if you think about it just like regular multiplication. Since multiplication is commutative and associative, we can rearrange this in a way that's easier to visualize: \[(7 \times 7)(\sqrt[3]{49} \times \sqrt[3]{7})\]
We can knock out that 7 * 7 = 49 right away and leave it alone for now. When we multiply the cube roots together, our result will be a cube root also- but try looking at it like this first:\[\sqrt[3]{49} \times \sqrt[3]{7} = \sqrt[3]{7 \times 49}\] which is the same thing as saying \[\sqrt[3]{7 \times 7 \times 7}\] Now that there are three of the same number under there, we can safely determine that our cube root is 7.
So now we have something that looks more like this:
\[49 \times 7\] And I'm sure you can take it from there ;)

Answer 6

okay i got \[\sqrt[3]{2}\] for this question and it was wrong.
\[\sqrt[3]{4} \times \sqrt[3]{32}\]

Answer 7

I dont know what I did wrong

Answer 8

The only thing missing is the 4 you pulled out from under the radical :) It's easy to forget to tack it back on there.

Answer 9

Thank you so so much

Answer 10

No problem :) glad I could help