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Question

If the square root of a number is between 6 and 7, then its cube root lies between:
  1. 2 and 3
  2. 4 and 4.5
  3. 2.5 and 3
  4. 3 and 4


Solution

The correct option is D 3 and 4
Let the given number be x
6<x<7
(Squaring the whole inequality)
36 < x < 49
(Taking cube roots of the inequality)
(36)13<(x)13<(49)13
We know, 2713=3<3613 & 4913<6413=4
3<x13<4
Cube root of x lies between 3 and 4.
 

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