SOLUTION: How do I determine Square roots? Example : I know that the square root of 484 is 22. How do you dtermine that or show how work is done.

Algebra ->  Square-cubic-other-roots -> SOLUTION: How do I determine Square roots? Example : I know that the square root of 484 is 22. How do you dtermine that or show how work is done.       Log On


   

Question 530694: How do I determine Square roots?
Example : I know that the square root of 484 is 22.
How do you dtermine that or show how work is done.
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
You can use a calculator to find square roots.
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Google has a built in calculator. Type sqrt(484) and it will reply 22.
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You can test various multiplicands to determine if they are square roots.
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There also is a old-fashioned long-hand "division" method you could learn.
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You can use the quadratic equation.
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The square of the square root minus the number = 0.
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x^2 - 484 = 0
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-484+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A1%2A-484=1936.

Discriminant d=1936 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+1936+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+1936+%29%29%2F2%5C1+=+22
x%5B2%5D+=+%28-%280%29-sqrt%28+1936+%29%29%2F2%5C1+=+-22

Quadratic expression 1x%5E2%2B0x%2B-484 can be factored:
1x%5E2%2B0x%2B-484+=+1%28x-22%29%2A%28x--22%29
Again, the answer is: 22, -22. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-484+%29