The video explains a method for quickly finding the square root of perfect squares less than 100. It involves identifying the square that corresponds to the units digit of the number and using the first digit of the square root to determine the remaining digit. The method requires knowledge of squares up to 9² and understanding that square roots can be both positive and negative. The video demonstrates the technique through various examples, emphasizing the need for practice to gain speed and accuracy.

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This article is a summary of a YouTube video “Square root in 3 seconds – math trick” by tecmath

Key insights

  • Fast Calculation Method: The video demonstrates a rapid technique for finding the square roots of perfect squares, particularly those less than 100. This method enables quick mental calculation without the need for extensive computation.
  • Knowledge of Squares Essential: A fundamental requirement for this method is a good understanding of the squares of numbers up to 9 (i.e., 1² to 9²). This knowledge is used to correlate the units digit of the number whose square root is being calculated with the corresponding square.
  • Dealing with Units and Tens Digits: The technique involves focusing on the units digit of the square root and matching it with the units digit of the number. This is followed by identifying the tens digit of the square root by considering the squares just under the leading digits of the number.
  • Positive and Negative Roots: The video stresses the importance of recognizing that square roots can have both positive and negative values. For example, the square root of a number like 576 can be both +24 and -24.
  • Practical Examples and Application: Through various examples, the video guides viewers on how to apply this technique in different scenarios, showing its practicality and efficiency in quickly calculating square roots.
  • Accuracy and Speed: The presenter emphasizes the importance of practice to improve speed and accuracy in using this method. As with any mental math technique, familiarity and frequent use enhance proficiency.
  • General Utility: The method is presented as a useful tool not just for academic purposes but also for everyday calculations where quick estimation of square roots might be needed.

Timestamped Summary

  • 0:00 – Introduction to the method of quickly finding the square roots of perfect squares, particularly those less than 100.
  • 0:19 – Example given to illustrate the method: calculating the square root of 576.
  • 1:00 – Emphasis on identifying square roots as both positive and negative values.
  • 1:16 – Explanation of the necessity of knowing the squares of numbers up to 9 for using this technique.
  • 1:48 – Demonstration of the method using the square root of 576, focusing on the units digit and leading digits.
  • 2:11 – Explanation of how to determine the first digit of the square root by comparing with squares below the leading digits of the number.
  • 2:36 – Method to decide between the two possible unit digits of the square root by multiplying the tens digit by the next higher number.
  • 3:22 – Application of the method to another example, calculating the square root of 1849.
  • 4:06 – Further examples to practice and illustrate the method, including square roots of 3364, 1444, and 8281.
  • 7:01 – Explanation of how the technique becomes faster with practice and familiarity.
  • 7:25 – Final example given for the square root of 2025, showing the simplicity in some cases.
  • 9:08 – Conclusion highlighting the effectiveness of the method and mentioning upcoming videos on calculating squares of any number.


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