Evaluate the following
2√28+3√63-√49
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
Simplify it into the product of an integer and a radical.
We do this by listing each product combo of 28
Check for integer square root values below:
√28 = √1√28
√28 = √2√14
√28 = √4√7
From that list, the highest factor with 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
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
Simplify it into the product of an integer and a radical.
We do this by listing each product combo of 63
Check for integer square root values below:
√63 = √1√63
√63 = √3√21
√63 = √7√9
From that list, the highest factor with 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
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
