QUESTION

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

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.

It can be mathematically expressed as:$36 < x < 49$
${{\left( 36 \right)}^{\dfrac{1}{3}}}<{{x}^{\dfrac{1}{3}}}<{{\left( 49 \right)}^{\dfrac{1}{3}}}$
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.