Calculate Square Root . . . using equations

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

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

Adding & Subtracting
Radicals

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Multiplying Radicals

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Dividing Radicals

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Rationalize the
Denominator

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Simplifying "Radicals"

$Math - Calculate Square Root Without Using a Calculator$

Calculate "Square Roots"
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$Math - Calculate Roots Using Equations$

Calculate Square Roots
Using Equations

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