square root chart — Definition, Formula & Examples
A square root chart is a reference table that lists numbers alongside their square roots, making it easy to look up values quickly instead of calculating them each time.
A square root chart is a tabular display of values and for a specified range of positive integers, typically presenting exact values for perfect squares and decimal approximations for non-perfect squares.
Key Formula
Where:
- = The non-negative number whose square root you are finding
- = The value that, when multiplied by itself, gives n
How It Works
To use a square root chart, find the number in the left column and read its square root in the right column. For perfect squares like 1, 4, 9, 16, 25, the square root is a whole number. For other numbers, the chart gives a rounded decimal approximation. Students often memorize the perfect square roots from through , then rely on the chart for non-perfect squares. Having these values at your fingertips speeds up work in algebra, geometry, and standardized tests.
Worked Example
Problem: Use a square root chart to simplify √50.
Step 1: Look up √50 on the chart. The approximate value is 7.071, but we want an exact simplified form.
Step 2: Factor 50 into a perfect square times another integer.
Step 3: Use the chart to find √25 = 5, then write the simplified radical.
Answer: √50 = 5√2 ≈ 7.071
Another Example
Problem: A square garden has an area of 81 square feet. What is the side length?
Step 1: The side length of a square equals the square root of its area.
Step 2: Look up 81 on the square root chart. Since 81 is a perfect square (9 × 9 = 81), the value is exact.
Answer: The side length is 9 feet.
Visualization
Why It Matters
Square root charts are a staple in pre-algebra and algebra 1 courses, where you simplify radicals, solve quadratic equations, and apply the Pythagorean theorem. Carpenters and engineers also reference square roots when calculating diagonal measurements and material dimensions. Having this chart committed to memory—or at least nearby—removes a common bottleneck in problem-solving.
Common Mistakes
Mistake: Confusing squaring with square rooting. For example, thinking √16 = 256 because 16² = 256.
Correction: √16 asks what number times itself gives 16. The answer is 4, because 4 × 4 = 16. Squaring and square rooting are inverse operations.
Mistake: Assuming every square root is a whole number.
Correction: Only perfect squares (1, 4, 9, 16, 25, …) have whole-number square roots. For all other positive integers, the square root is an irrational decimal. A chart helps you find or estimate these values.