Question

What is the square root of 2 as a power of 2?

Answer 1

Explanation:

x^(a/b)

means

`\sqrt[b]{ {x}^(a) }`

the numerator of the exponent is the actual "to the power of" factor.

the denominator defines the degree of the root to be taken.

as any integer number is also a fraction like

6 = 6/1

this applies to any form of rational numbers like

x^0.25 = x^(25/100) = x^(1/4) =

`\sqrt[4]{ {x}^(1) } = \sqrt[4]{x}`

with irrational numbers as exponents this gets trickier, as with infinite numbers without a pattern after the decimal point we have a problem to precisely specify the degree of the root, as we also have a problem to specify the irrational number itself.

we try to find the origin of the irrational number (like a square root)

`{x}^( √(3) )`

or

`\sqrt[ √(3) ]{ {x}^(2) } = {x}^(2 / √(3) )`

so,

`√(2) = \sqrt[2]{2} = {2}^(1 / 2)`

Answer 2

`2^{(1)/(2)}`

Explanation:

Taking the square root of a number is equivalent to putting that number to the power of 1/2.