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Square root of the sum of a number and 9 is 12. Find the Number.

  • Last Updated : 05 Aug, 2021
Geek Week

A system was introduced to define the numbers present from negative infinity to positive infinity. The system is known as the Number system. Number system is easily represented on a number line and Integers, whole numbers, natural numbers can be all defined on a number line. The number line contains positive numbers, negative numbers, and zero.

An equation is a mathematical statement that connects two algebraic expressions of equal values with ‘=’ sign.For example: In equation 3x+2 = 5, 3x+ 2 is the left-hand side expression and 5 is the right-hand side expression connected with the ‘=’ sign.

There are mainly 3 types of equations:

1- Linear Equation
2- Quadratic Equation
3- Polynomial Equation

Here, we will study about the Linear equations.



Linear equations in one variable are equations that are written as ax + b = 0, where a and b are two integers and x is a variable, and there is only one solution. 3x+2=5, for example, is a linear equation with only one variable. As a result, there is only one solution to this equation, which is x = 3/11. A linear equation in two variables, on the other hand, has two solutions.

A one-variable linear equation is one with a maximum of one variable of order one. The formula is ax + b = 0, using x as the variable.

There is just one solution to this equation. Here are a few examples:

  • 4x = 8
  • 5x + 10 = -20
  • 1 + 6x = 11

Linear equations in one variable are written in standard form as:

ax + b = 0

Here,

  • The numbers ‘a’ and ‘b’ are real.
  • Neither ‘a’ nor ‘b’ are equal to zero.

Solving Linear Equations in One Variable

The steps for solving an equation with only one variable are as follows:



Step 1: If there are any fractions, use LCM to remove them.

Step 2: Both sides of the equation should be simplified.

Step 3: Remove the variable from the equation.

Step 4: Make sure your response is correct.

Example: To get the Square of a number, we have to multiply the number by itself.

So, Square root is the number that on multiplication by itself gives the original number.  For example, a is the square root of b, then it is written as a=sqrt(b) or a = √b.  

For example, the square of 4 is 16, 42 = 16 and the square root of 16, sqrt(16) = 4. Since 16 is a perfect square, hence it is easy to find the square root of such numbers.

Example: What is the number when the square root of the sum of a number and 4 is 4?

Solution: 

Let the number be num.



According to the problem statement: Square of the sum of number i.e num and 4 is 4 i.e.

sqrt(num + 4)  = 4

To get the value of num, we have to solve this equation

On Squaring both sides, we get

sqrt(num+4) * sqrt(num+4) = 4 * 4
num + 4 = 16
num = 16-4
num = 12

So, the number is 12

Problem Statement: What is the number when the square root of the sum of a number and 9 is 12?

Solution: 

Let the number be num.

According to the problem statement:

The square root of the sum of number i.e num and 9 is 12 i.e.

sqrt(num + 9)  = 12

To get the value of num, we have to solve this equation 

On Squaring both sides, we get

sqrt(num+9) * sqrt(num+9) = 12 * 12
num + 9 = 144
num = 144-9
num = 135

So, the number is 135

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