Free square roots worksheet generator
Practice perfect square roots, simplify radical expressions, or find perfect cube roots.
What is a square root? How do you simplify one? ↓Your worksheet
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Math Practice
Paperloop MathAnswer key
What is a square root?
The principal square root of a nonnegative number is the nonnegative number that gives the original value when squared. For example, √49 = 7 because 7 × 7 = 49. A cube root reverses cubing: ∛125 = 5.
How do you simplify a square root?
Find a square factor
Look for the largest perfect square that divides the number under the radical.
Separate the factors
Rewrite the radical as a product, such as √(36 × 2).
Take the square root outside
Replace √36 with 6 and leave the square-free part under the radical.
Worked example: simplify √72
Since 72 = 36 × 2, rewrite √72 as √(36 × 2). Then √72 = √36 × √2 = 6√2. Check by squaring: (6√2)² = 36 × 2 = 72.
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Perfect squares
A square root asks which nonnegative number multiplied by itself gives the radicand. For example, √144 = 12.
Simplify a square root
Take square factors outside the radical: √72 = √(36 × 2) = 6√2. The remaining number under the root has no square factor.
Perfect cubes
A cube root reverses cubing. For example, ∛125 = 5 because 5 × 5 × 5 = 125.
Use the answer key
Exact answers
Radicals are shown in simplified form rather than as decimal approximations.