can smo reply asap? dis is rationalizing denominators: index 3 or higher how do u simplify dis? pls explain how u got the steps to the solution ty

Question

chocolateluva77 · Answer

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Tranquility · Answer

When you rationalize the denominator, you are trying to get rid of the cube root of the denominator. You need to multiply the numerator and denominator by $\sqrt[3]{225}$ twice so that way the cube root cancels out in the denominator

Essentially,
$\dfrac{2}{\sqrt[3]{225}} \times \dfrac{\sqrt[3]{225}}{\sqrt[3]{225}}  \times \dfrac{\sqrt[3]{225}}{\sqrt[3]{225}}  = ?$

chocolateluva77 · Answer

so what do u do after?

Tranquility · Answer

Simplify it

chocolateluva77 · Answer

how do u rationalize the denominator index 3√225

Tranquility · Answer

When you multiply the denominator across, you get

$ \left(\sqrt[3]{225} \right)^3$

What can you simplify that to?

chocolateluva77 · Answer

1 bruh idk

Tranquility · Answer

No... how?

Tranquility · Answer

cube root is the same thing as to the power of 1/3

$\sqrt[3]{x} = x^{\frac{1}{3}}$

Another way to write $(\sqrt[3]{225})^3$ would be as $ (225^{\frac{1}{3}})^3$

Can you simplify that now? All you have to do is multiply the exponents.

chocolateluva77 · Answer

is it (676/3) exponent 3?

Tranquility · Answer

no

Tranquility · Answer

$(\sqrt[3]{225})^3$ =  $ (225^{\frac{1}{3}})^3 = 225 ^{(\frac{1}{3} \times 3)} = ??$

chocolateluva77 · Answer

225

Tranquility · Answer

Exactly

Tranquility · Answer

$\dfrac{2}{\sqrt[3]{225}} \times \dfrac{\sqrt[3]{225}}{\sqrt[3]{225}}  \times \dfrac{\sqrt[3]{225}}{\sqrt[3]{225}}  = ?$

$ = \dfrac{2 \times \sqrt[3]{225} \times \sqrt[3]{225}}{225}$

Can you simplify the numerator?

I'll help start you off

$ = \dfrac{2 \times \sqrt[3]{225 \times 225}}{225}$

Remember that 225 is equal to 15 * 15
So we have 15 * 15 * 15 * 15 under the cube root. Can you factor out 15 from it?

Tranquility · Answer

Basically, you need to use this property:

$\large\sqrt[3]{x^3} = x$

chocolateluva77 · Answer

i don't get it 😭 how do i factor out 15?

Tranquility · Answer

We're only looking at the cube root right now

$ \sqrt[3]{225\times 225} = \sqrt[3]{15^3 \times 15} = \sqrt[3]{15^3} \times \sqrt[3]{15}$

Do you see it now?

chocolateluva77 · Answer

why did u do 15 exponent 3 × 15?

chocolateluva77 · Answer

15 exponent 3 is not 225

Tranquility · Answer

225 is 15 * 15

225 * 225 is going to be 15*15*15*15

which is 15^3 * 15

chocolateluva77 · Answer

so the answer is 2 index 3 √15/15

chocolateluva77 · Answer

dis is sm steps man is there a easier method?

chocolateluva77 · Answer

wya?

Tranquility · Answer

@chocolateluva77 wrote:

so the answer is 2 index 3 √15/15

Yes! $\dfrac{2\sqrt[3]{15}}{15}$

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