Question

hello, can you explain : 3 square root x^6 divided 3 square root 8x multiplied by 3 square root x^11. ???

Answer 1

Hm. Let me see if I have this right:

\[\frac{3\sqrt{x^6}}{3\sqrt{8x}} \cdot 3\sqrt{x^{11}}\]

Is that what the problem looks like?

Answer 2

the 3 sqroot x^11 is under the radicand.

Answer 3

Ok, gotcha. So we have:

\[\frac{3\sqrt{x^6}}{3\sqrt{8x}\cdot 3\sqrt{x^{11}}}\]

Answer 4

We can combine like terms by multiplying the 3s together and moving both of the bottom roots into the same one:

\[\frac{3\sqrt{x^6}}{9\sqrt{8x\cdot x^{11}}}\]

We see that we can combine the x terms in the denominator:

\[\frac{3\sqrt{x^6}}{9\sqrt{8x^{12}}}\]

Answer 5

thank you so very much!

Answer 6

Next, we can actually take the roots. Since we have even powers, that's easy:

\[\frac{3x^3}{9x^6\sqrt{8}}\]

Then we can divide properly for the powers and the 3/9:

\[\frac{1}{3x^3\sqrt{8}}\]

Answer 7

Finally, we can simplify \(\sqrt{8}\) by remembering that 8 is 4 * 2 and that we can take the square root of 4:

\[\frac{1}{3x^3(2\sqrt{2})}\]
\[\frac{1}{6x^3\sqrt{2}}\]

Answer 8

Most people also prefer keeping radicals out of the denominator; to do that, we can multiply by \(\sqrt{2}/\sqrt{2}\) and move the radical to the numerator:

\[\frac{1}{6x^3\sqrt{2}}\frac{\sqrt{2}}{\sqrt{2}}\]
\[\frac{\sqrt{2}}{6x^3\cdot 2}\]
\[\frac{\sqrt{2}}{12x^3}\]

Answer 9

No problem, glad to help :)

Answer 10

thanks!

Answer 11

Become a fan if you want! I'm trying to become a hero!