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

[mathdad]

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?

 

[MarkFL]

Your working assumes $0\le x$...it would be more proper to say:

$$\sqrt{12x^7}=2\left|x^3\right|\sqrt{3x}$$

Because:

$$|x|\equiv\sqrt{x^2}$$

 

[mathdad]

Your working assumes $0\le x$...it would be more proper to say:

$$\sqrt{12x^7}=2\left|x^3\right|\sqrt{3x}$$

Because:

$$|x|\equiv\sqrt{x^2}$$

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.