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Tuesday 20th of March
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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving an Equation That Contains a Square Root

An equation with a variable in a radicand is called a radical equation. Here are three examples:

The following procedure may be used to solve an equation that contains a variable under a square root symbol.

Procedure â€” To Solve an Equation That Contains a Variable Under a Square Root Symbol

Step 1 Isolate the square-root radical on one side of the equation.

Step 2 Square both sides of the equation.

Step 3 Solve for the variable.

Example 1

Solve:

 Solution Step 1 Isolate the square-root radical on one side of the equation. Add 3 to both sides of the equation. Step 2 Square both sides of the equation. Simplify. Step 3 Solve for the variable. Divide both sides by 2. x = 5 Step 4 Check the answer. To check, substitute 50 for x in the original equation and simplify.
So, x = 50 is the solution of the radical equation.

Example 2

Solve:

 Solution Step 1 Isolate the square-root radical on one side of the equation. Subtract 4 from both sides of the equation. Step 2 Square both sides of the equation. Simplify. Step 3 Solve for the variable. Add 5 to both sides of the equation. Divide both sides by 2. 2x = 54x = 27 Step 4 Check the answer. To check, substitute 27 for x in the original equation and simplify.

So, x = 27 is the solution of the radical equation.