Using Radicals to Solve Equations Worksheets

The square root is a specific case of a radical, representing the operation of taking the square root of a number. Radicals, on the other hand, encompass all roots, including square roots, cube roots, and so on. Surds are a type of radical representing irrational numbers expressed in root form.

Printable “Radical” worksheets:
Squares & square roots
Cubes & cube roots
Square Root Worksheets
Cube Root Worksheets

Simplify square roots (whole numbers or fractions)
Rationalizing the denominator (using radicals or conjugates)
Add & Subtract Radical Expressions
Multiply Radical Expressions
Divide Radical Expressions
Using Radicals to Solve Equations

Examples, solutions, videos, and worksheets to help Grade 6 and Grade 7 students learn how to use radicals to solve equations. Find the positive solutions to equations algebraically equivalent to equations of the form x²=p and x³=p.

How to Use Radicals to Solve Equations?

Equations that contain variables that are squared or cubed can be solved using the properties of equality and the definition of square and cube roots.

Simplify an equation until it is in the form of x² = p or x³ = p, where p is a positive rational number; then, take the square or cube root to determine the positive value of x.

Example:
Solve for x:
1/2 (2x²+10)=30
x²+5=30
x²+5-5=30-5
x²=25
√(x² )=√25
x=5

Have a look at this video if you need to review how to Using Radicals to Solve Equations.

• Using Radicals to Solve Equations

To Using Radicals to Solve Equations of fractions, you can simplify the numerator and denominator separately. Then, simplify the whole fraction if necessary.

Have a look at this video if you need to review how to Using Radicals to Solve Equationss of fractions.

• Simplify a square root of a rational number

Click on the following worksheet to get a printable pdf document.
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More Using Radicals to Solve Equations Worksheets

Printable
(Answers on the second page.)
(Square Roots)
Using Radicals to Solve Equations Worksheet #1
Using Radicals to Solve Equations Worksheet #2
Using Radicals to Solve Equations Worksheet #3
(Cube Roots)
Using Radicals to Solve Equations Worksheet #4
Using Radicals to Solve Equations Worksheet #5

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Using Radicals to solve Equations

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