Answer
Verified
40.8k+ views
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.
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.
Recently Updated Pages
Let gx 1 + x x and fx left beginarray20c 1x 0 0x 0 class 12 maths JEE_Main
The number of ways in which 5 boys and 3 girls can-class-12-maths-JEE_Main
Find dfracddxleft left sin x rightlog x right A left class 12 maths JEE_Main
Distance of the point x1y1z1from the line fracx x2l class 12 maths JEE_Main
In a box containing 100 eggs 10 eggs are rotten What class 12 maths JEE_Main
dfracddxex + 3log x A ex cdot x2x + 3 B ex cdot xx class 12 maths JEE_Main
Other Pages
Which of the following figures represent the variation class 12 physics JEE_Main
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
Amongst LiCl RbCl BeCl2 and MgCl2the compounds with class 11 chemistry JEE_Main
A food packet is dropped from a helicopter rising up class 11 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
In an electromagnetic wave A Power is equally transferred class 12 physics JEE_Main