How to calculate square roots fast and accurately: Master these techniques to save time in your next Math exam

Learning to calculate square roots quickly can make a huge difference in your maths exams. Whether you're doing algebra, geometry, or other topics, being fast and accurate with square roots gives you a real advantage. While calculators are handy, mental math tricks can save you time and deepen your understanding of maths. Many exams don’t permit calculators, so being well-versed in square root techniques can give you a serious edge.

Every second counts in maths exams. If you spend too long working out square roots, you’ll run out of time for other questions. Being quick with them helps you spot patterns and solve problems more easily. Some situations call for memorisation, while others require mental math techniques used by pros.

Here is a step-by-step explanation of how to tackle square root problems you may encounter in your next math exam:

Some essential square roots are better memorisedWhen tackling square roots of complex numbers in an exam, knowing some key square roots in advance can save both time and effort. Memorising squares from 1² to 20² (up to 400) allows you to instantly recognise perfect squares without relying on lengthy calculations. Here's a reference table to help you get started:


Smart tricks for tricky square rootsHere are some fun and smart tricks to deal with tricky square root problems with speed and accuracy:

The nearby perfect square trick

This works great when your number is close to a perfect square.

Example: To find √50, start with √49 = 7.

Use this formula: √50 ≈ 7 + (50-49)/(2×7) = 7 + 1/14 ≈ 7.07

The formula: √(a+difference) ≈ √a + difference/(2×√a)

This gives you accurate answers in seconds for numbers near perfect squares.

The weighted average method

When your number sits between two perfect squares, use this averaging trick.

Example: Find √45.

We know 6² = 36 and 7² = 49.

Since 45 is 9 away from 36 and 4 away from 49: Answer ≈ 6 + (45-36)/(49-36) × (7-6) = 6 + 9/13 ≈ 6.69

This gives you good answers without complicated maths.

Memory tricks for common roots

Some square roots have useful patterns you can memorise:

• √2 ≈ 1.414 (remember "I wish I knew" - count the letters: 1,4,1,4)
  
• √3 ≈ 1.732 (year of George Washington's birth)
  
• √5 ≈ 2.236

Which method to use whenChoose your method based on what type of number you're dealing with:


Advanced technique: Estimation by halvesFor quick estimates, use this simple rule; if you need √N, find the perfect squares on either side, then estimate roughly where N falls between them.

Example: √70 sits between √64 = 8 and √81 = 9. Since 70 is closer to 64, estimate around 8.4.

Practice makes perfectTo master these techniques, practice daily with different numbers, focusing on mental calculation rather than written work. Picture a number line in your mind, visualising where perfect squares sit and estimating positions between them. Time yourself regularly to simulate exam conditions and build confidence under pressure. Most importantly, apply these tricks when solving real algebra or geometry problems to reinforce your learning and make the skills second nature.

Calculating square roots doesn’t have to slow you down or cause stress. Methods like the nearby perfect square trick, weighted averaging, and memory patterns can make you much faster at mental maths.

The key is consistent practice. Start with easier numbers near perfect squares, then move on to more challenging ones. Within weeks, you’ll be answering square root questions quickly and confidently.