Question

Which of the following numbers is the fourth power of a natural number?
$(a){\text{ 6765201}}$
$(b){\text{ 6765206}}$
$(c){\text{ 6765207}}$
$(d){\text{ 6765209}}$

Answer 1

Hint: In the above given question, check for the fourth power of all the numbers given, then the number which is the fourth power of a natural number is the required solution.

Complete step-by-step answer:
Let us check for all the numbers given
$(a){\text{ 6765201}}$
Here, the natural number is 6765201.
The fourth power of the natural number can be given as
$\sqrt[4]{{6765201}} = 51$
$(b){\text{ 6765206}}$
Here, the natural number is 6765206.
The fourth power of the natural number can be given as
$\sqrt[4]{{6765206}} = 51.0000094$
$(c){\text{ 6765207}}$
Here, the natural number is 6765207.
The fourth power of the natural number can be given as
$\sqrt[4]{{6765207}} = 51.000011$
$(d){\text{ 6765209}}$
Here, the natural number is 6765209.
The fourth power of the natural number can be given as
$\sqrt[4]{{6765209}} = 51.000015$
Therefore, 6765201 is the fourth power of a natural number.
Hence, the correct answer is the option$(a)$.

Note: In order to solve the above given question, you must have an adequate knowledge about arithmetic and algebra. The fourth power of a number n is the result of multiplying four instances of n together.