Question

Square root of (4x^6)

Answer 1

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

Answer 2

No, not zero.

Answer 3

Simplify what amistre has written

Answer 4

Why did he divide the 6 by 2..?

Answer 5

those root radicals are just exponents

Answer 6

2rt() = ^1/2

10rt() = ^1/10

Answer 7

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

Answer 8

its makes the math simpler

Answer 9

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

Answer 10

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

Answer 11

\[ \sqrt{x} = x^{1/2} \]
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
\[ (x^{1/2})^2 = x^{2/2} = x^1 = x \]

Answer 12

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