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Expertly Reviewed by: David Chen, MS in Mathematics & Education Specialist

Learning how to get square root without calculator is a fundamental mathematical skill. Whether you are preparing for a test or simply curious about the logic behind the square root function, this calculator helps you find results and understand the step-by-step long division method.

Square Root Calculator

Result (√x):

How to Get Square Root Without Calculator Formula:

Long Division Method:

1. Group digits in pairs from the decimal point.
2. Find the largest integer whose square is less than or equal to the leftmost pair.
3. Subtract and bring down the next pair.

Source: Wolfram MathWorld, Khan Academy

Variables:

  • Number (x): The positive value for which you want to find the square root.
  • Radicand: The value inside the root symbol (√).
  • Quotient: In the long division method, this becomes the resulting square root.

Related Calculators:

What is how to get square root without calculator?

Finding a square root without a calculator usually refers to using the Long Division Method or the Estimation Method. Unlike basic division, the divisor changes in every step of this process, making it a unique algorithmic challenge.

This skill is essential for understanding the nature of irrational numbers and helps students build a stronger “number sense.” It allows you to estimate values like √2 or √10 quickly in your head by identifying the nearest perfect squares.

How to Calculate Square Root Without Calculator (Example):

Example: Find the square root of 625 manually.

  1. Group digits: Group 625 as 6 and 25.
  2. First digit: The largest square less than 6 is 4 (2²). Put 2 in the result.
  3. Subtract: 6 – 4 = 2. Bring down 25 to get 225.
  4. Next divisor: Double the current result (2 * 2 = 4). We need a digit ‘n’ such that 4n * n ≤ 225.
  5. Find ‘n’: If n=5, 45 * 5 = 225. Exact match!
  6. Final Result: The digits are 2 and 5, so √625 = 25.

Frequently Asked Questions (FAQ):

Q: What is the easiest way to estimate a square root?
A: Find the two closest perfect squares. For √20, it’s between √16 (4) and √25 (5), so it’s roughly 4.5.

Q: Can all numbers have square roots?
A: All non-negative real numbers have real square roots. Negative numbers have imaginary square roots.

Q: Is the manual method accurate?
A: Yes, the long division method can be carried out to as many decimal places as needed for precision.

Q: What is a perfect square?
A: A perfect square is an integer that is the square of another integer (e.g., 1, 4, 9, 16, 25).

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