 # sqrt(-58)

Evaluate √-58

## 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 72 = 49 and 82 = 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 = √158
58 = √229

From that list, the highest factor that has an integer square root is 1.
Therefore, we use the product combo √58 = √158
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 xth power denoted as nx (Write without exponents)
* n raised to the xth power raised to the yth power denoted as (nx)y (Write without exponents)
* Product of up to 5 square roots: √abcde
* 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?

1. √n2 = ±n

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### What 5 concepts are covered in the Square Roots and Exponents Calculator?

exponent
The power to raise a number
fraction
how many parts of a certain size exist
a/b where a is the numerator and b is the denominator
power
how many times to use the number in a multiplication
square root
a factor of a number that, when multiplied by itself, gives the original number
√x
square roots and exponents