anonymous
  • anonymous
how would you simplify a cubed root radical of 25 times the radical of 125
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
ok, you have 25^(1/3) * 125^(1/2)?
anonymous
  • anonymous
yes
anonymous
  • anonymous
ok, so how are 25 and 125 related?

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anonymous
  • anonymous
Both divisible by 5 and 25?
anonymous
  • anonymous
ok, cool, so 25 = 5^2 and 125 = 5^2
anonymous
  • anonymous
5^3, sorry
anonymous
  • anonymous
oh okay yeah
anonymous
  • 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
  • anonymous
omg it's too long for the page HAHA
anonymous
  • anonymous
what is the equation maker?
anonymous
  • anonymous
all right
anonymous
  • anonymous
the answer is 5^{13/6} sorry it's too long haha
anonymous
  • anonymous
yeah, that's how to do it easily hrwhyhry
anonymous
  • anonymous
okay.. how on earth did you get that though?
anonymous
  • anonymous
so you have 25=5^2, and 125=5^3....so you have (5^2)^(1/3) * (5^3)^(1/2)
anonymous
  • anonymous
you can then add the exponents...here: \[(5^2)^(1/3)\]
anonymous
  • anonymous
ohhhhh oka
anonymous
  • anonymous
y mn
anonymous
  • anonymous
(5^2)^(1/3) --> the square (2) and the (1/3) and now add together, 2/3
anonymous
  • anonymous
okay thank you so much!
anonymous
  • anonymous
so, you got it?
anonymous
  • anonymous
i think soooo
anonymous
  • anonymous
now how would you do x-\[\sqrt[3]{3}\div \sqrt{12}\]
anonymous
  • anonymous
sorry its supposed to be the x- the 3 one
anonymous
  • anonymous
????
anonymous
  • anonymous
just a second
anonymous
  • anonymous
thank you :)
anonymous
  • anonymous
\[(x-\sqrt[3]{3})/\sqrt{12}\]
anonymous
  • anonymous
is that the problem? is it equal to something?
anonymous
  • anonymous
no thats the problem. You only have to simplify it
anonymous
  • anonymous
ok
anonymous
  • anonymous
so what is sqrt(12)?
anonymous
  • anonymous
what are factors of 12?
anonymous
  • anonymous
the square root of 4 times the square root of 3?
anonymous
  • anonymous
right on, so sqrt(4) is simple, sqrt(3) is good because the problem has 3^(1/3)
anonymous
  • anonymous
is the answer 1 over x^1/6 times 2?
anonymous
  • anonymous
1/(x^1/6 * 2)?
anonymous
  • anonymous
yes
anonymous
  • anonymous
\[(x-(3^{1/3}))/(2*(3^{1/2}))\]
anonymous
  • anonymous
i had that... i just dont kmow if u can get rid of the three
anonymous
  • 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
  • anonymous
ok...
anonymous
  • anonymous
thank u for the help by the way
anonymous
  • anonymous
first look at 3^(1/3) / (2 * (3^1/2))
anonymous
  • anonymous
np
anonymous
  • anonymous
can you simplify that? focus on the 3's
anonymous
  • anonymous
u can divide 3 by 3 and get one right
anonymous
  • anonymous
when you divide by exponents you and subtract the exponents from values with the same base
anonymous
  • 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
  • anonymous
so you have 3^(-1/6)
anonymous
  • anonymous
which is 1/(3^1/6)
anonymous
  • anonymous
yes and u have to bring it below the division sign since it is negative?>
anonymous
  • anonymous
yeah, like in the last message
anonymous
  • anonymous
is the answer x over 3^1/6 *2
anonymous
  • anonymous
wait, x-1
anonymous
  • anonymous
(x-1)/(2*(3^1/6))
anonymous
  • anonymous
\[(x-1)/(2*(3^1/6))\]
anonymous
  • anonymous
\[(x-1)/(2*(3^{1/6}))\]
anonymous
  • anonymous
how's that look?
anonymous
  • anonymous
Thank you sooo much! I think thats right.....

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