Question

Create your own radical expression, containing a numerical coefficient and two different variables, which can be simplified. Explain, in complete sentences, how you developed the expression, the process of simplifying it, and provide the final simplified expression.

i just need someone to check this (:

Answer 1

\[\huge 7\sqrt[3]{1250x^{5}y^{3}}\]

Write out the prime factors of the radicand \[7\sqrt[3]{5 \times 5 \times 5 \times 5 \times 2 \times x \times x \times x \times x \times x \times y \times y \times y}\]Find three identical factors \[7\sqrt[3]{[5 \times 5 \times 5] \times 5 \times 2 \times [x \times x \times x] \times x \times x \times [y \times y \times y]}\]Merge the remaining factors and move the rest outside the radical\[35xy \sqrt[3]{10x^{2}}\]

Answer 2

Well done! <clap, clap>

If you want to be super clear you could say
\[\sqrt[3]{5\times5\times5\times5\times2\times x \times x \times x} = \sqrt[3]{5\times2}\sqrt[3]{5^3}\sqrt[3]{x^3} = 5x\sqrt[3]{10}\]

Answer 3

okay thanks @vf321 :)

Answer 4

you are 100% correct yummydum

You can also do it like this
\[\LARGE 7\sqrt[3]{1250x^5y^3}\]


\[\LARGE 7\sqrt[3]{10*125x^3*x^2*y^3}\]


\[\LARGE 7\sqrt[3]{125x^3y^3*10x^2}\]


\[\LARGE 7\sqrt[3]{5^3x^3y^3*10x^2}\]


\[\LARGE 7\sqrt[3]{(5xy)^3*10x^2}\]


\[\LARGE 7\sqrt[3]{(5xy)^3}*\sqrt[3]{10x^2}\]


\[\LARGE 7*(5xy)*\sqrt[3]{10x^2}\]


\[\LARGE 35xy\sqrt[3]{10x^2}\]

-----------------------------------------------------------

So \[\LARGE 7\sqrt[3]{1250x^5y^3}\] simplifies to \[\LARGE 35xy\sqrt[3]{10x^2}\]

Answer 5

wow thats a lot O.O
i think ill stick to factoring out to the primes all at once...but thanks anyway

THANKS GUYS!! :D

Answer 6

your method works as well...it may be longer/bigger, but if you're not sure how to factor like I did, then it's best to use your method

Answer 7

yw