Calculate Square Root . . . using equations

$logo for solving-math-problems.com$

$leftimage for solving-math-problems.com$

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).

Skip to example - click here

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

$Free Math Help$ $Math Help - Your Questions & Comments$ Skip to Free Math Help click here

$Math Help - Your Questions & Comments$ $Math Help - Your Questions & Comments$ Questions Others Have Asked click here

$Search this Site$ $Search this Site$ Search this Site click here

The Properties of Radicals & Roots - Real Numbers - click description

$Simplifying Radicals - Math - Radicals - adding and subtracting$

Adding & Subtracting
Radicals

$Math - Multiplying Radicals$

Multiplying Radicals

$Math - Dividing Radicals$

Dividing Radicals

$Math - Rationalizing the Denominator$

Rationalize the
Denominator

$Math - Fractional Exponents & Radicals$

Fractional Powers & Radicals

$Math - Simplifying Radicals$

Simplifying "Radicals"

$Math - Calculate Square Root Without Using a Calculator$

Calculate "Square Roots"
Without Using a Calculator

$Math - Calculate Roots Using Equations$

Calculate Square Roots
Using Equations

$Math - Free Videos on Radicals & Roots + Free Resources$

Videos
& Free Resources

$Return to Top of Page$ Return To "Top of Page" click here

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