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A squares calculator quickly computes the square (n²), square root (√n), and related properties of any number. Squares are fundamental in geometry, algebra, and statistics.
Fórmula
Perfect square: n² for integer n; Sum of first n squares = n(n+1)(2n+1)/6
- n
- Number to square
- n²
- Squared result (value)
Guía paso a paso
- 1n² = n × n
- 2√n: Newton's method or direct computation
- 3Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100...
- 4Difference of squares: a²−b² = (a+b)(a−b)
Ejemplos resueltos
Entrada
Square of 13
Resultado
13² = 169; √169 = 13
Entrada
Is 144 a perfect square?
Resultado
√144 = 12 exactly → yes, 12²=144
Preguntas frecuentes
What's the next perfect square after 100?
11² = 121. Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121...
How do I calculate 15² without calculator?
(10+5)² = 10² + 2(10)(5) + 5² = 100 + 100 + 25 = 225.
What's the sum of first 10 perfect squares?
1+4+9+16+25+36+49+64+81+100 = 10(11)(21)/6 = 385.