Determinar la suma de cifras de un número elevado al cuadrado

MathematicsNumber TheoryMedium

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6. Si $\overline{abc} \times a = 1068$; $\overline{abc} \times b = 1780$; $\overline{abc} \times c = 2136$, determina la suma de cifras de $\overline{abc}^2$.

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Step 2

Nos piden calcular la suma de las cifras de abc al cuadrado. Sabemos que el número abc, denotado con una barra superior, se descompone como cien por a, más diez por b, más c.

$$\overline{abc} = 100a + 10b + c$$
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Step 3

Por lo tanto, elevar abc al cuadrado es equivalente a multiplicar abc por cien a, más abc por diez b, más abc por c.

$$\overline{abc}^2 = \overline{abc} \times (100a + 10b + c)$$
$$\overline{abc}^2 = 100(\overline{abc} \times a) + 10(\overline{abc} \times b) + (\overline{abc} \times c)$$
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Step 4

Ahora, sustituimos los valores dados en el problema: abc por a es mil sesenta y ocho, abc por b es mil setecientos ochenta, y abc por c es dos mil ciento treinta y seis.

$$\overline{abc}^2 = 100(1068) + 10(1780) + 2136$$

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About This Question

Subject
Mathematics
Topic
Number Theory
Difficulty
Medium
Question Type
Open Ended

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