Question

A natural number is greater than three times its square root by 4. Find the number

Answer 1

Hint: Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity and are also used for counting purpose. It does not include zero or negative numbers. 1 is the smallest natural number and 0 is the smallest whole number. But there is no largest whole number or natural number because each number has its successor.
The square root of a number n is a value that, when multiplied by itself, gives the number.
In a number of problems, there are some clues about one or more numbers, and we can use these clues to form an equation that represents the problem mathematically.
To solve this question read the question carefully, choose a variable to represent the number. Translate the problem into an equation. Solve the equation and check the answer using the equation formed.
Complete step-by-step answer:
Let the natural number be x
According to the question, x is greater than three times its square root by 4,
$\begin{gathered}
  x = 3\sqrt x + 4 \\
  x - 4 = 3\sqrt x \ldots \left( 1 \right) \\
\end{gathered} $
On squaring both the sides, we get,
$\begin{gathered}
  {\left( {x - 4} \right)^2} = {\left( {3\sqrt x } \right)^2} \\
  {x^2} + 16 - 8x = 9x \\
  {x^2} - 8x - 9x + 16 = 0 \\
  {x^2} - 17x + 16 = 0 \\
  {x^2} - 16x - x + 16 = 0 \\
  x\left( {x - 16} \right) - 1\left( {x - 16} \right) = 0 \\
  \left( {x - 16} \right)\left( {x - 1} \right) = 0 \\
  x = 1,16{\text{ }}\left( {{\text{Natural number}}} \right) \\
\end{gathered} $
On checking, by putting the value of x in equation (1) only x=16 will satisfy the equation.
Hence, the number is 16.

Note: To solve these types of questions, reasoning must be performed based on common sense knowledge and the information provided by the source problem. Some word problems ask to find two or more numbers. We will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.