SOLUTION: Can you please help me? I have tried working it out but it doesn't check out right. (x+7)^3/2=27

Question 123339: Can you please help me? I have tried working it out but it doesn't check out right.
(x+7)^3/2=27
Found 3 solutions by Earlsdon, bucky, MathLover1:
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Solve for x:
Raise both sides to the 2/3 power.

Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!
The way you wrote your problem it could be interpreted in several ways. It could be:
.

.
But I suspect that you meant:
.

.
So I am going to work the second version in which the exponent is . If I am not correct
you will probably need to post your problem again.
.
Starting with:
.

.
You can use the power rule of exponents to rewrite the problem as:
.

.
Notice that on the right side the 27 is equivalent to . Substitute 3 cubed for 27
and the equation then becomes:
.

.
Take the cube root of both sides and the equation reduces to:
.

.
Square both sides and the equation is then:
.

.
Subtract 7 from both sides and you have:
.

.
Check ... return to the original problem:
.

.
Substitute 2 for 7 and you have:
.

.
Combine the 2 + 7 to get 9 and the problem then is:
.

.
You can then take the square root of 9 and cube it or cube 9 and take the square root of that
with the same result. The square root of 9 is 3 and if you cube 3 you get 27, making the
equation become 27 = 27. Or you can cube 9 and get 729. Then take the square root of 729
and get 27 ... again making the equation 27 = 27. Or, since 3/2 = 1.5, you can use a calculator
and raise 9 to the 1.5 power and you again get 27 ... once more making the equation 27 = 27.
.
In any case x = 2 is a valid solution to the problem.
.
Hope this helps you to understand the problem and how to work it through to a solution.
.

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

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