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Square Root Calculator

📊 Square Root Calculator

Quickly determine the square root of any number with accuracy.

Result will appear here…

📌 What is a Square Root?

The square root of a number is a value that, when multiplied by itself, gives the original number.

Example: The square root of 25 is 5, since 5 × 5 = 25.

📌 Methods to Calculate Square Root

  • Prime Factorization Method: Express the number as a product of prime factors, then take the square root of each pair.
  • Long Division Method: A manual method used for precise square root calculations.
  • Estimation Method: Approximating the square root using nearby perfect squares.

📌 Examples of Square Root Calculations

MethodExampleSolution
Prime Factorization3636 = 2² × 3² → Square root = 2 × 3 = 6
Long Division144Using long division, √144 = 12
Estimation50√49 = 7 and √64 = 8, so √50 ≈ 7.1

❓ FAQs

Q1: How do I calculate the square root?
✅ Use prime factorization, long division, or estimation methods.

Q2: Can square roots be negative?
✅ The principal square root is always positive, but negative roots exist in complex numbers.

Q3: Can I calculate the square root of a fraction?
✅ Yes, take the square root of both the numerator and denominator separately.

Q4: Why are square roots important?
✅ Square roots are used in physics, engineering, and financial calculations.

Q5: How do I find the square root of a non-perfect square?
✅ Use approximation methods or a calculator.

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