Term 1 has a square root, so we evaluate and simplify:
Simplify 2√28.
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, so we try simplify it into the product of an integer and a radical.
We do this by listing each product combo of 28 checking for integer square root values below: √28 = √1√28 √28 = √2√14 √28 = √4√7
From that list, the highest factor that has an integer square root is 4. Therefore, we use the product combo √28 = √4√7 Evaluating square roots, we see that √4 = 2
Simplifying our product of radicals, we get our answer:
Multiply by our constant of 2
2√28 = (2 x 2)√7 2√28 = 4√7
Term 2 has a square root, so we evaluate and simplify:
Simplify 3√63.
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 63 checking for integer square root values below: √63 = √1√63 √63 = √3√21 √63 = √7√9
From that list, the highest factor that has an integer square root is 9. Therefore, we use the product combo √63 = √9√7 Evaluating square roots, we see that √9 = 3
Simplifying our product of radicals, we get our answer:
Multiply by our constant of 3
3√63 = (3 x 3)√7 3√63 = 9√7
Term 3 has a square root, so we evaluate and simplify:
Simplify -1√49.
If you use a guess and check method, you see that 62 = 36 and 82 = 64. Since 36 < 49 < 64 the next logical step would be checking 72.
72 = 7 x 7 72 = 49 <--- We match our original number!!! Multiplying by our outside constant, we get -1 x 7 = -7 Therefore, -1√49 = ±-7
The principal root is the positive square root, so we have a principal root of -7
Group constants
-7 = -7
Group square root terms for 13
(4 + 9)√7 13√7
Build final answer:
-7 + 13√7
How does the Square Roots and Exponents Calculator work?
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.
What 3 formulas are used for the Square Roots and Exponents Calculator?
