4th root is same as square root of square root: sqrt(256) = 16, and sqrt(16) = 4
16.
16 x 16 = 256
The idea is to take out perfect squares. The largest perfect square in this case is 256, which is the square of 16 (if you have trouble figuring this out, you can take out a smaller perfect square first, and then see if you find additional perfect squares). In any case, the end result should not have a factor that is a perfect square. Using the symbol "root()" for square root: root(512) = root(256 x 2) = root(256) x root(2) = 16 root(2)
It has no pure square root. 16 x 16 =256 but this leaves a remainder of 24.
162 is 256 and 172 is 289, so YES, √266 is irrational
Not necessarily. The square root of 2.56 equals 1.6, and the square root of 0.25 equals 0.5, for two examples. If the decimal represents a rational number that is a fraction of two perfect squares, then the square root will be a rational number. The two examples I gave were 2.56 = 256/100, and 0.25 = 1/4.
16 or -16The square root of 256 is 16. 16
No, irrational numbers must continue past the decimal indefinitely, without a pattern, and can't be expressed as a fraction. Not only does 2.56 stop at the hundredth decimal, but it can also be expressed as the fraction 256/100. Its worth noting that 1.999999...forever repeating is also a rational number. Irrational numbers are usually things like pi, the square root of two, etc.
Yes.
4th root is same as square root of square root: sqrt(256) = 16, and sqrt(16) = 4
2.56 = 256 / 100 therefore, root (2.56) = root (256) / root (100) =16/10=1.6
The square root of 65536 is equal to 256.
Look for the largest square number in its factors. The square root of 512 is equal to the square root of 2 times the square root of 256. The square root of 256 is 16. The square root of 512 simplifies to 16 times the square root of 2.
16.
16 is a perfect square (of 4) and the square root of 256.
16 x 16 = 256