Square Root of 1024
The square root of 1024 is 32, because 32 × 32 = 1024. Since 1024 is a perfect square, its square root is a whole number.
By prime factorisation
1024 = 2¹⁰. To take a square root, halve the exponent: √(2¹⁰) = 2⁵ = 32. This is the quickest route whenever a number is a clean power of 2.
Grouping the factors in pairs shows the same thing: 1024 = (2 × 2 × 2 × 2 × 2) × (2 × 2 × 2 × 2 × 2) = 32 × 32.
Worked examples
Confirm √1024 = 32.
- 32 × 32 = 32 × 30 + 32 × 2
- = 960 + 64
- = 1024. ✓
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Related concepts
Frequently asked questions
It is 32, since 32² = 1024.
Yes. 1024 = 2¹⁰ = 32², so it is a perfect square.