## anonymous 4 years ago Square root of (4x^6)

1. amistre64

sqrt(4) * x^(6/2)

2. JamesJ

No, not zero.

3. JamesJ

Simplify what amistre has written

4. anonymous

Why did he divide the 6 by 2..?

5. amistre64

those root radicals are just exponents

6. amistre64

2rt() = ^1/2 10rt() = ^1/10

7. JamesJ

because $(x^a)^b = x^{ab}$ Hence $\sqrt{x^6} = (x^6)^{1/2} = x^{6/2} = ...$

8. amistre64

its makes the math simpler

9. JamesJ

Hence here $\sqrt{4x^6} = \sqrt{4} \sqrt{x^6} = ... what?$

10. anonymous

I still don't get where the 1/2 is coming from

11. JamesJ

$\sqrt{x} = x^{1/2}$ For example, if $\sqrt{x} = 3$ then $\sqrt{x}^2 = 3^2$ i.e., $x = 3^2$ It must be therefore that $$\sqrt{x} = x^{1/2}$$. If this weren't the case we wouldn't have $\sqrt{x}^2 = x$ Having $\sqrt{x} = x^{1/2}$ is consistent with the definition of square root because $(x^{1/2})^2 = x^{2/2} = x^1 = x$

12. anonymous

So am i only dividing the x^6 by two to make it x^3 since the exponent doesn't pertain to the 4?