Year 8: Approximation of the square root

This cheat sheet helps you quickly approximate the square root of a number without using a calculator.

Methods for Approximation

1. Estimation Based on Perfect Squares

Look for perfect squares close to your number. This is the quickest method.

• If your number is between two perfect squares, the square root will be between their square roots.
• Example: √27 - 27 is between 25 (√25 = 5) and 36 (√36 = 6). Therefore, √27 is approximately 5.2 or 5.3.

2. The "Guess and Check" Method

Start with a guess, then adjust it based on the result.

• If the square of your guess is too high, choose a smaller number.
• If your guess is too low, choose a larger number.
• Keep refining your guess until you get close enough to the actual square root.

3. Rounding

Round the square root to the nearest whole number or decimal place depending on the accuracy needed.

Remember, approximation is about getting a reasonable answer, not a perfect one.