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Calculate Square Roots . . . using equations
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* Example *
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* Simplify the Square Root Calculation *
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*Calculate Square Root*:

*Step 1:*

*Factor* the radicand *into* a series of *perfect squares*.

*Step 2:*

*Evaluate* the square root of *each perfect square separately* - __thus removing every perfect square from beneath the square root radical__.

Note: while each square root has two solutions (+ and -), it is only necessary to show the positive values in this step.

*Step 3:*

*Evaluate the SURD* . Once the perfect squares have been removed from beneath the square root radical, evaluate the surd (the remaining, unevaluated square root) using standard methods such as Newton's Method, Direct Calculation, a Square Root Table, or the Guess & Check Method.

*Step 4:*

*Multiply* all the *results obtained separately* (in steps 2 & 3).

The final answer is:
to 4 decimal points

* Example *
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* Factor the Square Root Equation *
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*Calculate Square Root*:

*Step 1:*

*Square each side* of the *equation*.

*Step 2:*

*Re-write* the *equation* shown in step 1 in standard *quadratic form*.

*Step 3:*

*Factor* the quadratic *equation*.

*Step 4:*

Using the Zero-Product Principle, set the *first factor* equal to zero, then *solve for x*.

*(The Zero-Product Principle states that when two factors multiplied together equal zero, either one factor or both factors must equal zero.)*

*Step 5:*

Set the *second factor* equal to zero, then *solve for x*.

The final answer is:

(The square root has a *different solution for each factor*.)