SOLUTION: I am having a hard time solving this problem. The {{{sqrt(x^3) = 8}}}. Thanks for your time.

Algebra ->  Expressions-with-variables -> SOLUTION: I am having a hard time solving this problem. The {{{sqrt(x^3) = 8}}}. Thanks for your time.      Log On


   

Question 51437: I am having a hard time solving this problem.
The sqrt%28x%5E3%29+=+8.
Thanks for your time.
Found 2 solutions by rchill, vanetiks:
Answer by rchill(405) About Me  (Show Source):
You can put this solution on YOUR website!
If the square root of something is 8, that means the something must be 64 because 8*8=64. The something in this case is x%5E3, which means x%5E3=64. That means we need to find the cube root of 64; i.e., some number multiplied by itself three times is equal to 64. To do that:
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=4.
  • Graphical form: x%5E3=64 simplifies to %2Bx%5E2%2B4%2Ax%2B16=0
  • Text form: x^3=64 simplifies to +x^2+4*x+16=0
  • Cartoon (animation) form: simplify_cartoon%28+x%5E3=64+%29
    For tutors: simplify_cartoon( x^3=64 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%5E3=highlight_red%28+64+%29.
Moved these terms to the left highlight_green%28+-64+%29
It becomes x%5E3-highlight_green%28+64+%29=0.
Look at highlight_red%28+x%5E3-64+%29=0.
Divided polynomial on the left by known factors (x-(4))
It becomes %2Bhighlight_green%28+x%5E2%2B4%2Ax%2B16+%29=0.
Result: %2Bx%5E2%2B4%2Ax%2B16=0
This is an equation! Solutions: x=4.

Universal Simplifier and Solver


Done!

Answer by vanetiks(6) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt(x3) = 8
sqrt(x) = 4
x = 4