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Calculate Square Root
. . .
Using Equations




Calculate Square Root - Using Equations . . . Introduction - Using Equations to Calculate Square Roots:

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

http://javascript.internet.com/math-related/amazing-quadratic-equation-solver.html



Return to Exponents, Radicals, & Roots Page Return to Exponents, Radicals, & Roots Page Return to Exponents, Radicals, & Roots Page Return To "Exponents, Radicals, & Roots" click here




The Properties of Radicals & Roots - Real Numbers - click description
Simplifying Radicals - Math - Radicals - adding and subtracting
Math - Multiplying Radicals
Math - Dividing Radicals
Math - Rationalizing the Denominator
Math - Fractional Exponents & Radicals
Math - Simplifying Radicals
Math - Calculate Square Root Without Using a Calculator
Math - Calculate Roots Using Equations
Math - Free Videos on Radicals & Roots + Free Resources
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Calculate Square Roots . . . using equations



Example - Simplify the Square Root Calculation


Math - Simplifying Square Root Expressions - example 1 Calculate Square Root: Math - Simplifying Square Root Expressions - Initial Problem - example 1

Step 1:

Factor the radicand into a series of perfect squares.

Math - Simplifying Square Root Expressions - example 1 - Factor the radicand into a series of perfect squares - Step 1


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.

Math - Simplifying Square Root Expressions - example 1 - Evaluate the square root of each perfect square separately  - Step 2


Step 3:

Evaluate the SURD 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.

Math - Simplifying Square Root Expressions - example 1 - Evaluate the SURD - Step 3


Step 4:

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

Math - Simplifying Square Root Expressions - example 1 - Multiply all the results obtained separately - Step 4



The final answer is: Math - Simplifying Square Root Expressions - Final Answer - example 1 to 4 decimal points




Example - Factor the Square Root Equation


Math - Factoring the Square Root Equation - example 2 Calculate Square Root: Math - Factoring the Square Root Equation - Initial Problem - example 2

Step 1:

Square each side of the equation.

Math - Factoring the Square Root Equation - example 2 - Square each side of the equation - Step 1

Step 2:

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

Math - Factoring the Square Root Equation - example 2 - Re-write the equation shown in step 1 in standard quadratic form - Step 2

Step 3:

Factor the quadratic equation.

Math - Factoring the Square Root Equation - example 2 - Factor the quadratic equation - Step 3

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.)

Math - Factoring the Square Root Equation - example 2 - Solve 1st factor - Step 4

Step 5:

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

Math - Factoring the Square Root Equation - example 2 - Solve 2nd factor - Step 5



The final answer is: Math - Factoring the Square Root Equation - Final Answer - example 2

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







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