How do you write the square root of 3 in exponential form? or any other radical into exponential form
To write the square root of 3 in exponential form, we can use the property of exponents that states:
a^(1/n) = nth root of a
In this case, "a" is 3 and "n" is 2 (since we are taking the square root).
Therefore, the square root of 3 in exponential form is:
3^(1/2)
This means that the square root of 3 is the number that, when raised to the power of 2, equals 3.
To write the square root of a number in exponential form, we can use the concept of fractional exponents.
For example, to write the square root of 3 in exponential form, we can express it as 3^(1/2). Here, the base is 3, and the exponent is 1/2, which represents the square root.
Similarly, for any other radical, we can use the exponent that corresponds to the root.
For instance, the cube root of 5 can be written as 5^(1/3), where the base is 5 and the exponent is 1/3, representing the cube root.
In general, to write the nth root of a number in exponential form, we use the base raised to the power of 1 divided by n.
since (x^a)^b = x^(ab)
(√3)^2 = 3
So, if √3 = 3^a,
(3^a)^2 = 3^(2a) = 3^1
So, 2a=1
√3 = 3^(1/2)
The nth root of x is x^(1/n)