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Mathematics 15 Online
OpenStudy (anonymous):

cubedroot250+cubedroot54-cubedroot16 ( i hope i wrote that right? @SolomonZelman lol

OpenStudy (anonymous):

@MaxwellSmart

OpenStudy (solomonzelman):

Yes, you did:) \(\normalsize\color{blue}{ \sqrt[3]{250}+\sqrt[3]{54}-\sqrt[3]{16} }\)

OpenStudy (anonymous):

yes thats it!

OpenStudy (yanasidlinskiy):

Bam!!!!!!

OpenStudy (anonymous):

\(\LARGE \sqrt[3]{250} + \sqrt[3]{54} - \sqrt[3]{16} \)

OpenStudy (solomonzelman):

\(\normalsize\color{blue}{ \sqrt[3]{5^3 \times 2}+\sqrt[3]{3^3 \times 2 }-\sqrt[3]{2^3 \times 2} }\)

OpenStudy (solomonzelman):

Almost a sequence :)

OpenStudy (anonymous):

sorry guys i dont write it out like that...i dont have the sqrt symbol :(

OpenStudy (anonymous):

In order to combine the roots together, they have to be roots of the same number.

OpenStudy (yanasidlinskiy):

Equation editor has it:)

OpenStudy (solomonzelman):

1) Click ALT and Hold it, 2) Click 2 5 1 on the number pad, on the bottom right corner of your keyboard. 3) release ALT.

OpenStudy (solomonzelman):

This √

OpenStudy (anonymous):

dont we have to take the cubed root?

OpenStudy (anonymous):

Let's do the problem.

OpenStudy (anonymous):

okay

OpenStudy (solomonzelman):

\(\normalsize\color{black}{ \sqrt[3]{5^3 \times 2}+\sqrt[3]{3^3 \times 2 }-\sqrt[3]{2^3 \times 2} }\) I broke it down :)

OpenStudy (solomonzelman):

I would almost imagine something like \[\sum_{n=1}^{5}~~\sqrt[3]{2(6-n)^3}\]

OpenStudy (anonymous):

dont i break down the 250?

OpenStudy (solomonzelman):

yes 5³ × 2

OpenStudy (anonymous):

make the radican the same bu simplifying?

OpenStudy (anonymous):

\(\LARGE \sqrt[3]{250} + \sqrt[3]{54} - \sqrt[3]{16} \) \(\LARGE =\sqrt[3]{125 \times 2} + \sqrt[3]{27 \times 2} - \sqrt[3]{8 \times 2} \) \(\LARGE =\sqrt[3]{125} \times \sqrt[3]{2} + \sqrt[3]{27} \times \sqrt[3]{2} - \sqrt[3]{8} \times \sqrt[3]{2} \) \(\LARGE =5\sqrt[3]{2} + 3 \sqrt[3]{2} - 2\sqrt[3]{2} \) Now you have the same roots.

OpenStudy (solomonzelman):

Rule: \(\Large\color{black}{ \sqrt[a]{b^a}=\sqrt[\cancel{ a }]{b^\cancel{ a }}=b }\)

OpenStudy (anonymous):

oh haha! i see!

OpenStudy (anonymous):

thank you @MaxwellSmart and @SolomonZelman

OpenStudy (anonymous):

yw

OpenStudy (solomonzelman):

anytime

OpenStudy (anonymous):

wait? does it need to be simplified?

OpenStudy (anonymous):

factor out whats common @MaxwellSmart

OpenStudy (anonymous):

:( sorry

OpenStudy (anonymous):

Since the roots are all the same, they are now like terms. Now you can combine them together.

OpenStudy (anonymous):

combine what though?

OpenStudy (anonymous):

Just like 5a + 3a - 2a = 6a

OpenStudy (anonymous):

oh...duh you just showed me that

OpenStudy (anonymous):

thanks again!

OpenStudy (anonymous):

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