Term 1 has a square root, so we evaluate and simplify:

A negative square root needs to use imaginary numbers:

The imaginary number i is denoted as √-1 Simplify √-58.

Since -58 is less than 0, we have an imaginary number of i where i = √-1 We can express this as √58√-1 Since √-1 = i, we have √58i Simplify √58.

Checking square roots, we see that 7^{2} = 49 and 8^{2} = 64. Our answer in decimal format is between 7 and 8 Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

We do this by listing each product combo of 58 checking for integer square root values below: √58 = √1√58 √58 = √2√29

From that list, the highest factor that has an integer square root is 1. Therefore, we use the product combo √58 = √1√58 Evaluating square roots, we see that √1 = 1

Since 1 is the greatest common factor, this square root cannot be simplified any further:

Multiply by our constant of 1

√58 = √58

√58i = ±sqrt(58)i

How does the Square Roots and Exponents Calculator work?

Free Square Roots and Exponents Calculator - Given a number (n), or a fraction (n/m), and/or an exponent (x), or product of up to 5 radicals, this determines the following: * The square root of n denoted as √n
* The square root of the fraction n/m denoted as √n/m
* n raised to the x^{th} power denoted as n^{x} (Write without exponents)
* n raised to the x^{th} power raised to the yth power denoted as (n^{x})^{y} (Write without exponents)
* Product of up to 5 square roots: √a√b√c√d√e
* Write a numeric expression such as 8x8x8x8x8 in exponential form This calculator has 1 input.

What 3 formulas are used for the Square Roots and Exponents Calculator?