SOLUTION: Solve for x, check for any extraneous solutions. 2x^(3/2) -8=46 I tried solving this problem where it is 54 ^2/3. I put this in the calculator and it didn't turn out as a whole

Algebra ->  Rational-functions -> SOLUTION: Solve for x, check for any extraneous solutions. 2x^(3/2) -8=46 I tried solving this problem where it is 54 ^2/3. I put this in the calculator and it didn't turn out as a whole      Log On


   

Question 1019755: Solve for x, check for any extraneous solutions.
2x^(3/2) -8=46
I tried solving this problem where it is 54 ^2/3. I put this in the calculator and it didn't turn out as a whole number. Is it still correct or did I do something wrong?
Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
You did something wrong.

matrix%282%2C1%2C%22%22%2C2x%5E%283%2F2%29+-8=46%29

Add 8 to both sides:

matrix%282%2C1%2C%22%22%2C2x%5E%283%2F2%29=54%29

Divide both sides by 2

matrix%282%2C1%2C%22%22%2Cx%5E%283%2F2%29+=27%29

We want to get x to the 1 power, so to do that,
we raise both sides to the reciprocal of 3%2F2
power, which is the 2%2F3 power.  So we raise
both sides to the 2%2F3 power.

matrix%282%2C1%2C%22%22%2C%28x%5E%283%2F2%29%29%5E%282%2F3%29+=27%5E%282%2F3%29%29

Multiply the exponents to remove the parentheses on
the left.  Multiplying expr%283%2F2%29%2Aexpr%282%2F3%29=1

On the right use the principle matrix%282%2C1%2C%22%22%2CA%5E%28B%2FC%29+=%28root%28C%2CA%29%29%5EB%29

x%5E1+=%28root%283%2C27%29%29%5E2

x+=+3%5E2

x=9 

Edwin

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2x^(3/2) -8=46
2x^(3/2) = 54
x^(3/2) = 27
x^3 = 729
x = 9