Vedic Math: Calculating Square Roots for any number

Vedic Math Trick for Mental Calculation

This is a fast mental math trick to estimate square roots:

1. Find the nearest perfect square

2. Use the formula: 
   

3. $$\sqrt{N} \approx \sqrt{\text{Base}} + \frac{(N - \text{Base})}{2 \times \sqrt{\text{Base}}}$$

   Works best for numbers close to perfect squares.

Example: Find √82

• Nearest perfect square: 81 (√81 = 9)

• Use the formula:
  
  

  $$\sqrt{82} \approx 9 + \frac{(82 - 81)}{2 \times 9}$$ $$= 9 + \frac{1}{18} \approx 9.06$$

✅ Final Answer: √82 ≈ 9.06