Square Root Chart from 1 to 100

You need a square root chart for a test, for homework, or to check a calculation. This gives you the decimal and radical form for every integer from 1 to 100, a perfect squares list, and instructions for using the table to estimate other roots. Print the chart for quick reference. Keep a copy on your desk or in your binder.

The table below shows the principal square root of each integer from 1 to 100. The first column gives the number (the radicand). The second column gives the square root in decimal form, rounded to four decimal places. The third column shows the simplest radical form when the radicand is not a perfect square, that is, an expression a√b where b has no perfect square factor greater than 1.

For perfect squares, the radical form is a whole number. For example, √25 = 5. For a non-perfect square like 2, the simplest radical form is √2, which is an irrational number. The decimal 1.4142 is an approximation; the exact value is √2. When you need precision in algebra, use the radical form. When you need a practical measurement, use the decimal.

The perfect squares list gives every integer from 1 to 20 squared, because square roots of perfect squares are whole numbers. Memorising these makes algebra faster. If you see √144, you know it is 12 without reaching for a calculator.

1² = 1, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49, 8² = 64, 9² = 81, 10² = 100, 11² = 121, 12² = 144, 13² = 169, 14² = 196, 15² = 225, 16² = 256, 17² = 289, 18² = 324, 19² = 361, 20² = 400.

Beyond 20, extend the pattern: 25² = 625, 30² = 900, 40² = 1600, 50² = 2500, 100² = 10000. The square root of 400 is 20. The square root of 900 is 30. The square root of 1600 is 40. The square root of 2500 is 50. The square root of 10000 is 100.

Use the square root table to estimate roots for numbers outside the 1-100 range. Suppose you need √150. Find the nearest perfect squares: 144 (√144 = 12) and 169 (√169 = 13). Since 150 is closer to 144, √150 is about 12.2 or 12.3. For √200, use the squares 169 (13) and 225 (15); the root falls near 14.14.

This estimation method fails when the radicand is negative. The square root of a negative number is not a real number but an imaginary one, defined by the imaginary unit i. For √(-4), the answer is 2i. The chart above only covers non-negative radicands.

Keep this printed reference at your desk.

The print stylesheet removes the background and shrinks the table to fit one sheet. Use it during tests that allow notes, for homework checks, or as a quick lookup on the wall.

When you print, the table above prints in landscape orientation on A4 or letter paper. The font size stays readable at 10pt. The heading remains at the top. No extra margins. If your printer cuts off the right column, set the page to landscape in your printer settings first.