how would you simplify a cubed root radical of 25 times the radical of 125

- anonymous

how would you simplify a cubed root radical of 25 times the radical of 125

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- anonymous

ok, you have 25^(1/3) * 125^(1/2)?

- anonymous

yes

- anonymous

ok, so how are 25 and 125 related?

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## More answers

- anonymous

Both divisible by 5 and 25?

- anonymous

ok, cool, so 25 = 5^2 and 125 = 5^2

- anonymous

5^3, sorry

- anonymous

oh okay yeah

- anonymous

\[\sqrt[3]{25} \times \sqrt{125} = 25^{1/3} \times 125^{1/2} = 5^{2/3} \times 5^{3/2} = 5^{4/6} \times 5^{9/6} = 5^{13/6}\]
Feel free to correct me, this is my first time using this equation maker.

- anonymous

omg it's too long for the page HAHA

- anonymous

what is the equation maker?

- anonymous

all right

- anonymous

the answer is 5^{13/6} sorry it's too long haha

- anonymous

yeah, that's how to do it easily hrwhyhry

- anonymous

okay.. how on earth did you get that though?

- anonymous

so you have 25=5^2, and 125=5^3....so you have (5^2)^(1/3) * (5^3)^(1/2)

- anonymous

you can then add the exponents...here: \[(5^2)^(1/3)\]

- anonymous

ohhhhh oka

- anonymous

y
mn

- anonymous

(5^2)^(1/3) --> the square (2) and the (1/3) and now add together, 2/3

- anonymous

okay thank you so much!

- anonymous

so, you got it?

- anonymous

i think soooo

- anonymous

now how would you do x-\[\sqrt[3]{3}\div \sqrt{12}\]

- anonymous

sorry its supposed to be the x- the 3 one

- anonymous

????

- anonymous

just a second

- anonymous

thank you :)

- anonymous

\[(x-\sqrt[3]{3})/\sqrt{12}\]

- anonymous

is that the problem? is it equal to something?

- anonymous

no thats the problem. You only have to simplify it

- anonymous

ok

- anonymous

so what is sqrt(12)?

- anonymous

what are factors of 12?

- anonymous

the square root of 4 times the square root of 3?

- anonymous

right on, so sqrt(4) is simple, sqrt(3) is good because the problem has 3^(1/3)

- anonymous

is the answer 1 over x^1/6 times 2?

- anonymous

1/(x^1/6 * 2)?

- anonymous

yes

- anonymous

\[(x-(3^{1/3}))/(2*(3^{1/2}))\]

- anonymous

i had that... i just dont kmow if u can get rid of the three

- anonymous

so you can separate x and -3^(1/3) because they have the same denominator and they are part of a subtraction operation

- anonymous

ok...

- anonymous

thank u for the help by the way

- anonymous

first look at 3^(1/3) / (2 * (3^1/2))

- anonymous

np

- anonymous

can you simplify that? focus on the 3's

- anonymous

u can divide 3 by 3 and get one right

- anonymous

when you divide by exponents you and subtract the exponents from values with the same base

- anonymous

so 3^(1/3) / 3^(1/2) is 3^(1/3) * 3^-(1/2)...can you can add these exponents --> 1/3 = 2/6, 1/2 = 3/6, need to have similar fractions....so 2/6 - 3/6 = -1/6

- anonymous

so you have 3^(-1/6)

- anonymous

which is 1/(3^1/6)

- anonymous

yes and u have to bring it below the division sign since it is negative?>

- anonymous

yeah, like in the last message

- anonymous

is the answer x over 3^1/6 *2

- anonymous

wait, x-1

- anonymous

(x-1)/(2*(3^1/6))

- anonymous

\[(x-1)/(2*(3^1/6))\]

- anonymous

\[(x-1)/(2*(3^{1/6}))\]

- anonymous

how's that look?

- anonymous

Thank you sooo much! I think thats right.....

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