what is the square root of (4x^6) simplified?

Question

e.mccormick · Answer

$$\sqrt{4x^6}$$?

geerky42 · Answer

4 = 2², $\large x^6 = (x^3)^2$ so $\sqrt{4x^6} = \boxed{|2x^3|}$

geerky42 · Answer

Is this clear? @BridgetF

anonymous · Answer

sorry, I still dont understand

e.mccormick · Answer

OK.  What he has done is change 4 into 2 squared and the x to the 6th to x to the 3rd that is squared.  Do you know the power rules for doing that?  Or is the confusion elsewhere?

anonymous · Answer

The confusion is everywhere. I dont seem to get any of this. I am exhausted from thinking and not understanding

e.mccormick · Answer

That's OK.  It happens.  By the power rules, a power times a power is the powers added and a power to a power is the powers multipled.  For example:
$$a^2\times a^3 = a^{2+3} = a^5 \;and\; (b^3)^5=b^{3 \times 5}=b^{15}$$

Geerky42 was using those rules to play around with things.  That made the 4 into 2 squared and that other thing he did: $$(x^3)^2$$

anonymous · Answer

why is it an absolute value at the end?

e.mccormick · Answer

Because of the square root and powers of 2  Any power of 2 will make something positive.  so (-1)^2 is 1 and (-2)^2 is 4 and so on.  Because of that, the answer would always be positive.

anonymous · Answer

Thanks for your help :-)

e.mccormick · Answer

np. I hope that all makes more sense now. If not, you may want to look into the atributes of exponents. Here is a site that has all sorts of stuff like this written out a little different than most books: http://www.purplemath.com/modules/exponent.htm I find the second way of talking about it helps me.