Question

What is the probability of finding numbers from 1 to 1000 such that they are squares, cubes or both of a natural number?​

Answer 1

Answer:

25+25=50 and square root is 25 ...,.. 5

Answer 2

Answer:

the probability of perfect square and perfect cube numbers from 1 to 1000 is $\frac{19}{500}$ = 0.038

Step-by-step explanation:

from 1 to 1000, there are 31 perfect square numbers.

they are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 , 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900 and 961

from 1 to 1000 there are 10 perfect cube numbers including 1000

they are 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000

there are 38 perfect square and perfect cube numbers between 1 and 1000

(excluding the repeated numbers)

there are total 1000 numbers from 1 to 1000

∴ n= 1000

therefore the probability of perfect square and perfect cube numbers from 1 to 1000 is $\frac{38}{1000}$

  =$\frac{19}{500}$

= 0.038