¿Cuantos enteros positivos tienen el mismo numero de cifras en la representación decimal de sus cuadrados y cubos?

3 positive integers.

Step-by-step explanation:

This can be translated to:

"how many integer numbers have the same number of digits in their cubes and squares?"

for example, a number that will be an option is 2:

Because 2*2 = 4

               2*2*2 = 8

the square and cube of 2 have the same number of digits.

3 for example:

3*3 = 9

3*3*3 = 27

does not match the condition.

1 does match it, obviusly.

0 is not positive, so we can ignore it.

let's see 4.

4*4 = 16

4*4*4 = 64

So 4 is other number that matches the condition.

Now, 5:

5*5 = 25

5*5*5 = 125

5 does not match the condition, and any number upper than 5 also does not match the condition.

so the numbers we have are 1, 2 and 4.

so we have 3 integers.

its 8

step-by-step explanation:

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl