SOLUTION: Hello could you help me with this problem by explaining it step by step please. Simplify the following root:∛40b^4

Algebra ->  Square-cubic-other-roots -> SOLUTION: Hello could you help me with this problem by explaining it step by step please. Simplify the following root:∛40b^4       Log On


   

Question 950832: Hello could you help me with this problem by explaining it step by step please.
Simplify the following root:∛40b^4
Found 2 solutions by MathLover1, jim_thompson5910:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

root%283%2C40b%5E4%29+......first write 40 as 8%2A5, and b%5E4 as b%5E3%2Ab

root%283%2C8%2A5b%5E3%2Ab%29+......write 8 as 2%5E3
root%283%2C2%5E3%2A5b%5E3%2Ab%29+.........write a root of product as root%283%2C2%5E3%29%2Aroot%283%2C5%29root%283%2Cb%5E3%29%2Aroot%283%2Cb%29+......root%283%2C2%5E3%29=2 and root%283%2Cb%5E3%29=b
2b%2Aroot%283%2C5%29root%283%2Cb+%29
2b%2Aroot%283%2C5b%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
root%283%2C40b%5E4%29+=+root%283%2C8%2A5b%5E4%29 Factor 40 into 8*5


root%283%2C40b%5E4%29+=+root%283%2C8%2A5b%5E3%2Ab%29 Factor b%5E4 into b%5E3%2Ab


root%283%2C40b%5E4%29+=+root%283%2C8b%5E3%2A5b%29 Rearrange terms.


root%283%2C40b%5E4%29+=+root%283%2C8b%5E3%29%2Aroot%283%2C5b%29 Break up the root.


root%283%2C40b%5E4%29+=+root%283%2C%282b%29%5E3%29%2Aroot%283%2C5b%29 Rewrite 8b%5E3 as %282b%29%5E3.


root%283%2C40b%5E4%29+=+2b%2Aroot%283%2C5b%29 Take the cube root of %282b%29%5E3 to get 2b
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