Evaluate the following
√5√7
Term 1 has a square root, so we evaluate and simplify:
We have a product of 2 square root terms
The product of square roots is equal to the square root of the products
√5√7 = √5*7
√5√7 = √35
Simplify √35.
Checking square roots, we see that
52 = 25 and 62 = 36
Our answer in decimal format is between 5 and 6
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 35
Check for integer square root values below:
√35 = √1√35
√35 = √5√7
From that list, the highest factor with an integer square root is 1
Therefore, we use the product combo √35 = √1√35
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√35
Final Answer:
1√35
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
