document.write( "Question 51437: I am having a hard time solving this problem.
\n" ); document.write( "The $\"sqrt%28x%5E3%29+=+8\"$ .
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Algebra.Com's Answer #34384 by rchill(405) $\"\"$ $\"About$

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:
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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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.

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DETAILED EXPLANATION

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Look at $\"x%5E3=highlight_red%28+64+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-64+%29\"$
It becomes $\"x%5E3-highlight_green%28+64+%29=0\"$ .
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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: $\"%2Bx%5E2%2B4%2Ax%2B16=0\"$
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Universal Simplifier and Solver

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Done!

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