To understand what [tex]\( 256^{\frac{1}{2}} \)[/tex] means, we need to break down the notation and the mathematical concept behind it.
The exponent [tex]\( \frac{1}{2} \)[/tex] signifies taking the square root of a number. In general, for any positive number [tex]\( x \)[/tex], [tex]\( x^{\frac{1}{2}} \)[/tex] is equivalent to [tex]\(\sqrt{x}\)[/tex], which means the square root of [tex]\( x \)[/tex].
Let's apply this to the given number:
[tex]\[
256^{\frac{1}{2}} = \sqrt{256}
\][/tex]
Next, we need to find the square root of 256. We know that the square root of a number is a value that, when multiplied by itself, gives the original number. For 256, that number is 16 because:
[tex]\[
16 \times 16 = 256
\][/tex]
Thus,
[tex]\[
\sqrt{256} = 16
\][/tex]
So, [tex]\( 256^{\frac{1}{2}} = 16 \)[/tex].
Given this understanding, we can identify [tex]\( 256^{\frac{1}{2}} \)[/tex] as the square root of 256. Therefore, the correct answer among the provided options is:
(D) Square root of 256.
