Question

How many positive numbers from 1 to 200 both inclusive are equal to the cube of an integer?
(a) 6
(b) 5
(c) 4
(d) 1

Answer 1

Hint: Find the cube root of each integer starting from 1 and check how many interger’s cube fall under the interval given in question.

Complete step-by-step answer:
Cubing of integers from 1 to 5 will have their cubes in the interval 1 to 200.
\[ \Rightarrow {(1)^3} = 1;{(2)^3} = 8;{(3)^3} = 27;{(4)^3} = 64;{(5)^3} = 125\]
Cube of 6 will give 216 which will not fall in the given interval.
There are such 5 positive numbers (1,2,3,4,5).

Note: Everyone should remember the cube roots of integers. Remembering cube roots will help us in solving such questions easily without getting into lengthy calculations.