Evaluate the following
√112
Term 1 has a square root, so we evaluate and simplify:
Simplify √112.
Checking square roots, we see that
102 = 100 and 112 = 121
Our answer in decimal format is between 10 and 11
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 112
Check for integer square root values below:
√112 = √1√112
√112 = √2√56
√112 = √4√28
√112 = √7√16
√112 = √8√14
From that list, the highest factor with an integer square root is 16
Therefore, we use the product combo √112 = √16√7
Evaluating square roots, we see that √16 = 4
Simplifying our product of radicals, we get our answer:
Group square root terms for 4
4√7
Final Answer:
4√7
Common Core State Standards In This Lesson
6.EE.A.1
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: √a√b√c√d√e
* Write a numeric expression such as 8x8x8x8x8 in exponential form
This calculator has 1 input.
* 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?
√n2 = ±n
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
