Simplify Square Root 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
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 simplify square roots or simplify radicals.

How to simplify square roots?

There are two sets of simplify square roots worksheets.

• simplify square roots of whole numbers
• simplify square roots of fractions

To simplify square roots, you need to factor out any perfect squares from the radicand, which is the number under the radical symbol √.

You can follow these general guidelines to simplify square roots:

• Identify perfect square factors: Look for perfect square factors. For example, in the square root of 48, you can identify the perfect square factor of 16 because 16 × 3 = 48.
• Break down the number: Express the number inside the square root as the product of the perfect square factor and any remaining factors. For example, √48 = √(16 × 3).
• Simplify each factor: Take the square root of each perfect square factor. In our example, √(16 × 3) becomes √16 × √3, which simplifies to 4√3 since the square root of 16 is 4.

Here is another example of simplifying square roots using the perfect square method or the prime factors method.
 

If the radicand does not have any perfect squares, then the square root cannot be simplified. For example, the square root of 19 cannot be simplified.

Memorizing the perfect squares up to 100 will help you in simplifying square roots.

Have a look at this video if you need to review how to simplify square roots.

• Simplify Square Roots

To simplify square root 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 simplify square roots of fractions.

• Simplify a square root of a rational number

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Simplify Square Root Worksheets.

 

More Simplify Square Root Worksheets

Printable
(Answers on the second page.)
Simplify Square Root Worksheet #1 (whole numbers)
Simplify Square Root Worksheet #2 (fractions)

(With step-by-step Solutions)
Simplify Square Root Worksheet #3
Simplify Square Root Worksheet #4
Simplify Square Root Worksheet #5

Related Lessons & Worksheets

Squares & square roots
Cubes & cube roots

Whole number exponents
Negative whole number exponents
Unit fraction exponents (positive or negative)
Fractional exponents (positive or negative)

Simplify Square Roots
Simplify Square Roots with Fractions

More Printable Worksheets

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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