How much is 2 to the power of 1/2?

By using the multiplication rule of exponents and power we will solve this question. The exponent of any number represents how many times to use the number in a multiplication.

Answer: 2 to the power of 1/2 is √2 or 1.4142…

Let's solve this question step by step.

Explanation:

Given that, 2 to the power of 1/2

Basically, the rules for exponentiation states that If n is a positive integer and x is any real number, then aⁿ can be represented as:

aⁿ = a × a × … × a (n times)

Hence 2 to the power of 1/2 can be written as 2^(1/2) which is a fractional exponent.

Where the number 2 is called the base, whereas (1/2) is the power or exponent of the expression. Any exponent of (1/2) is actually the square root of that number.

Therefore, 2^(1/2) = √2 or 1.4142…

Hence, 2 to the power of 1/2 is √2 or 1.4142…