Evaluate the following
√-58
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 = √-1We 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
Simplify it into the product of an integer and a radical.
We do this by listing each product combo of 58
Check for integer square root values below:
√58 = √1√58
√58 = √2√29
From that list, the highest factor with 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
√58i = ±sqrt(58)iFrom that list, the highest factor with 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
Group square root terms for 1
1√-58
Final Answer:
Common Core State Standards In This Lesson
How does the Square Roots and Exponents Calculator work?
* 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: √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?
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
