Equations can be used to calculate the square root of a number.

• Simplify the Square Root Calculation. To simplify the square root calculation:
  
  
  1) Factor the radicand into a series of perfect squares
  
  
  2) Evaluate the square root of each perfect square separately - thus removing every perfect square from beneath the square root radical.
  
  
  3) 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.
  
  
  4) Multiply all the results obtained separately (in steps 2 & 3).
  
  
  
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Simplify a Square Root Calculation - free ON-LINE Calculator Compute a simplified square root for any number. Practice simplifying a square root radical, and check your work using these on-line calculators:

http://www.mathwarehouse.com/arithmetic/square-root-calculator.php

http://www.webmath.com/simpsqrt.html

• Factor the Square Root Equation Equations can be used to evaluate square roots by setting the equation equal to zero, then factoring the equation. This method works well for numbers which are perfect squares, but is very difficult to use when calculating the square root of a number which is not a perfect square. However, factoring has the advantage of identifying both positive and negative roots.
  
  
  Skip to example - click here

Compute a Square Root by Factoring the Square Root Equation - free ON-LINE Calculator. Practice factoring a square root equation, and check your work using these on-line calculators:

http://www.algebrahelp.com/calculators/equation/factoring/

http://www.freemathhelp.com/factoring-calculator.php

http://www.basic-mathematics.com/factoring-calculator.html

Calculate Square Root . . .
using equations

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Example - Simplify the Square Root Calculation
Factor the radicand into a series of perfect squares (to the maximum extent possible).

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 remaining 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

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Example - Re-write the equation in standard quadratic form.
Solve the quadratic equation to find the roots.

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.)