How do you simplify sqrt{12x^7}?

  • #1
mathdad
1,283
1
Simplify sqrt{12x^7}

Solution:

sqrt{4•3•x^6•x}

2x^3(sqrt{3x})

Is this correct?

Note 1:

According to wolfram, the answer is 2sqrt{3}•sqrt{x^7}

Note 2:

The term x^3 in my answer comes from the breakdown of sqrt{x^7} as sqrt{x^6•x}. Isn't sqrt{x^6} the same as x^3?
 
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  • #2
Your working assumes $0\le x$...it would be more proper to say:

\(\displaystyle \sqrt{12x^7}=2\left|x^3\right|\sqrt{3x}\)

Because:

\(\displaystyle |x|\equiv\sqrt{x^2}\)
 
  • #3
MarkFL said:
Your working assumes $0\le x$...it would be more proper to say:

\(\displaystyle \sqrt{12x^7}=2\left|x^3\right|\sqrt{3x}\)

Because:

\(\displaystyle |x|\equiv\sqrt{x^2}\)

Back in high school over 30 years ago, my teachers never taught to include the absolute value to a square root problem. For me sqrt{x^2} = x not the |x| but of course, you are right.
 

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