📊 Square Root Calculator
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📌 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
Method | Example | Solution |
---|---|---|
Prime Factorization | 36 | 36 = 2² × 3² → Square root = 2 × 3 = 6 |
Long Division | 144 | Using long division, √144 = 12 |
Estimation | 50 | √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.