Question & Answer

If the square root of a number is between 6 and 7, then its cube root lies between
A.2, 3
B.2.5, 3
C.3, 4
D.4, 4.5

ANSWER Verified Verified
 Hint: Mathematics includes the study of topics which are related to quantity, structure, space and change. For solving this problem, we first form an equation using the first part of the problem statement. Then we find the range of x. After that we can easily calculate the range of cube roots.

Complete step by step answer:
As per our question, we are given that the square root of a number lies between 6 and 7.
The square of 6 is 36.
The square of 7 is 49.
So, the number lies between 36 and 49.
It can be mathematically expressed as:$36 < x < 49$
Now taking the cube root of whole equation, we get
${{\left( 36 \right)}^{\dfrac{1}{3}}}<{{x}^{\dfrac{1}{3}}}<{{\left( 49 \right)}^{\dfrac{1}{3}}}$
The approximate value of ${{\left( 36 \right)}^{\dfrac{1}{3}}}$ is 3.302.
The approximate value of ${{\left( 49 \right)}^{\dfrac{1}{3}}}$ is 3.659.
Therefore, the cube root of the number lies between 3 and 4.
Hence option (c) is correct.

Note: The key concept involved in this question is the basic formulation of the problem statement into equation. Once the equation is established, we easily obtain our result. This knowledge is helpful in solving complex equations.