Understanding the Context

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 × 4 = 16. The square root symbol is √, so √64 refers to the principal (non-negative) square root of 64.

What Is the Square Root of 64?

The square root of 64 is 8.

This is because:
8 × 8 = 64

Key Insights

So, √64 = 8.

It’s important to note that every positive number has two square roots: one positive (8) and one negative (−8), since both ×8 and ×(–8) yield 64. However, by convention, the square root symbol √ returns the original positive root—especially in basic math contexts. So when asked for the square root of 64, we say 8.

How to Calculate √64

You can find the square root of 64 in several ways:

1. By Factoring

We know 64 = 8 × 8, so √64 = 8.

Final Thoughts

2. Using a Calculator

Simply input “√64” on any scientific calculator to get the result instantly: √64 = 8.

3. Estimation and Rounding

If you don’t have a calculator, you can estimate:

• 8² = 64 → so √64 = 8
  
• 9² = 81 > 64, so the root must be less than 9
  Hence, the closest integer and exact value is 8.

Why Is the Square Root of 64 Important?

Understanding exact square roots like √64 builds a strong foundation in arithmetic and algebra. Square roots appear in various fields such as:

• Geometry: Calculating the diagonal of a square (e.g., a square with side 8 units has a diagonal of 8√2, derived from √64 in related formulas).
  
• Physics: Finding distances or scaling factors in equations.
  
• Finance & Engineering: Simplifying complex formulas involving area and volume.

Moreover, knowing √64 = 8 helps improve mental math skills and prepares learners for radicals and irrational numbers.