Trucos de raíz cuadrada
sin trucos de raíz cuadrada, En el mundo de las matemáticas, las raíces cuadradas se presentan a menudo como retos formidables, que hacen reflexionar incluso a las mentes más brillantes.
Sin embargo, dominar los trucos de raíz cuadrada fir calcular raíces cuadradas puede ser una habilidad potenciadora, no sólo para los entusiastas de las matemáticas, sino para cualquiera que busque agudizar sus habilidades matemáticas mentales.
En este artículo, nos adentraremos en el fascinante mundo de los trucos para calcular raíces cuadradas que te ayudarán a calcularlas rápidamente y sin esfuerzo.
¿Qué es la raíz cuadrada?
La raíz cuadrada de un número es el valor que multiplicado por sí mismo da el número original. Supongamos que 5 multiplicado por 5 da 25. Así que podemos decir que 5 es el valor de la raíz cuadrada de 25.
Del mismo modo, 4 es el valor de la raíz de 16, 6 es el valor de la raíz de 36, 7 es el valor de la raíz de 49, etc. Dado que el cuadrado representa el área de un cuadrado que es igual a ‘lado x lado’, por lo tanto, la raíz cuadrada representa la longitud del lado del cuadrado. El símbolo de la raíz cuadrada se denota por ‘√’. Por lo tanto, los números de raíz cuadrada se representan como √4, √5, √8, √9, etc.
Para utilizar la calculadora, haga clic aquí
El truco de raíz cuadrada de la estimación
La estimación es una herramienta poderosa cuando se trata de raíces cuadradas. Trucos de raíz cuadrada para la estimación
La regla de oro
Un truco útil para encontrar la raíz cuadrada es recordar que la raíz cuadrada de cualquier número comprendido entre dos cuadrados perfectos consecutivos caerá entre las raíces cuadradas de esos dos cuadrados perfectos. Por ejemplo, si necesitas hallar la raíz cuadrada de 20, sabes que cae entre las raíces cuadradas de 16 (4) y 25 (5). Por tanto, la raíz cuadrada de 20 es aproximadamente 4,5.
Aproximación con fracciones
En Trucos de raíz cuadrada También puedes estimar raíces cuadradas convirtiéndolas en fracciones. Este método puede ser increíblemente útil cuando se trata de números cuadrados no perfectos.
Supongamos que quieres hallar la raíz cuadrada de 7. Empieza por reconocer que 7 está entre 4 y 9. Luego exprésalo como fracción, 7/9. Luego, exprésalo como una fracción, 7/9. Ahora, puedes estimar la raíz cuadrada como √(7/9), que se simplifica a (√7) / 3, dándote una buena aproximación.
Factorización de números primos Trucos de raíz cuadrada
Un método para calcular raíces cuadradas es descomponer el número en sus factores primos. Este método puede ser especialmente útil para números grandes. Por ejemplo, vamos a hallar la raíz cuadrada de 36. Primero, identifica los factores primos: 36 = 2^2 * 3^2. Ahora, toma uno de cada factor primo del interior de la raíz cuadrada, lo que resulta en √(2^2 * 3^2) = 2 * 3 = 6.
Tabla de raíces cuadradas de 1 a 50
También puedes memorizar la tabla de raíces cuadradas de los números del 1 al 50, para resolver problemas basados en ellas. Aquí tienes la lista disponible:
Number | Square Root Value(√) |
1 | 1 |
2 | 1.414 |
3 | 1.732 |
4 | 2 |
5 | 2.236 |
6 | 2.449 |
7 | 2.646 |
8 | 2.828 |
9 | 3 |
10 | 3.162 |
11 | 3.317 |
12 | 3.464 |
13 | 3.606 |
14 | 3.742 |
15 | 3.873 |
16 | 4 |
17 | 4.123 |
18 | 4.243 |
19 | 4.359 |
20 | 4.472 |
21 | 4.583 |
22 | 4.69 |
23 | 4.796 |
24 | 4.899 |
25 | 5 |
26 | 5.099 |
27 | 5.196 |
28 | 5.292 |
29 | 5.385 |
30 | 5.477 |
31 | 5.568 |
32 | 5.657 |
33 | 5.745 |
34 | 5.831 |
35 | 5.916 |
36 | 6 |
37 | 6.083 |
38 | 6.164 |
39 | 6.245 |
40 | 6.325 |
41 | 6.403 |
42 | 6.481 |
43 | 6.557 |
44 | 6.633 |
45 | 6.708 |
46 | 6.782 |
47 | 6.856 |
48 | 6.928 |
49 | 7 |
50 | 7.071 |
Trucos de raíz cuadrada para números de 2 cifras
Los trucos para hallar la raíz cuadrada de cuadrados perfectos son muy fáciles de recordar. Tenemos que tener en cuenta el dígito unitario de los cuadrados de los números del 1 al 10. Encuentra los dígitos unitarios que obtenemos después de elevar al cuadrado los números del 1 al 10 en la siguiente tabla.
Number | Unit digit of Number2 |
1 | 1 |
2 | 4 |
3 | 9 |
4 | 6 |
5 | 5 |
6 | 6 |
7 | 9 |
8 | 4 |
9 | 1 |
10 | 0 |
Por lo tanto, de la tabla anterior podemos deducir que si cualquier cuadrado perfecto termina con los dígitos anteriores en el lugar de la unidad, entonces su raíz cuadrada tendrá el mismo número respectivo en el lugar de la unidad.
Por ejemplo, la raíz cuadrada de 81 es 9.
Trucos de raíz cuadrada de números de 3 cifras
La raíz cuadrada de un número de tres cifras es siempre un número de dos cifras. Aprendamos a hallar la raíz cuadrada con un ejemplo.
Trucos de raíz cuadrada 1
La raíz cuadrada de 144:
- Empareja los dígitos del lado derecho: 1 44
- El lugar unitario de 144 es 4. Por lo tanto, la raíz cuadrada tendrá 2 u 8 en el lugar unitario.
- Ahora, considerando el primer dígito, 1, es el cuadrado de 1. Así, el primer dígito de la raíz cuadrada de 144 es 1.
- Puesto que 1 es el más pequeño del cuadrado. Por lo tanto, la raíz cuadrada de 144 tomará un número más pequeño entre 2 y 8. Por lo tanto, será 2.
Por lo tanto, la raíz - cuadrada requerida es 12.
Trucos de raíz cuadrada 2
Trucos de raíz cuadrada, el punto a tener en cuenta
- es que la raíz cuadrada de 3 dígitos es 2 dígitos.
- toma pares de izquierda a derecha un par y un solo.
empieza por la izquierda en el caso de 144 es 1 por la izquierda. - la clave es recordar el ultimo digito de los numeros cuadrados.
como 1×1=1, 2×2=4,3×3=9,4×4=16,5×5=25,6×6=36,7×7=49,8×8=64,9×9=81 y asi sucesivamente. - ahora el cercano a 1 es 1×1 mientras que el cercano al par 44 que es 4 en ultimo es o 2×2=4 o 8×8=64.
- pero 8×8=64 es definitivamente un número grande así que será 2×2=4 el ans de 144 de 12.
Trucos de raíz cuadrada de números de 4 cifras
Vamos a profundizar en la raíz cuadrada del número 4624.
Paso 1: El dígito de la unidad en este número es 4, que puede ser un dígito de la unidad de su número raíz cuadrada como 2 u 8. Porque 2×2 es 4 y 8×8 es 64.
Paso 2: Ahora vamos a considerar los dos primeros dígitos que es 46 que viene entre los cuadrados de 6 es 42.
Paso 3: Ahora, tenemos que encontrar entre 62 o 68 que es la raíz cuadrada de 4624.
Paso 4: Puesto que el dígito de la decena es 6 y el siguiente número es 2, tenemos que multiplicar ambos números como 6 x 2 = 12, y puesto que 12 es menor que 24.
Paso 5: La raíz cuadrada de 4624 será el número mayor entre 62 y 68, es decir, 68.
Por lo tanto, √4624 = 68.
Herramientas y aplicaciones digitales
Calculadora de Alicia es una de las mejores herramientas para encontrar la raíz cuadrada de cualquier número porque ralentiza los pasos involucrados en ella junto con diferentes esquemas de color para diferentes partes.
para utilizar la calculadora vaya a la página principal o haga clic aquí.
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