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If the square root of a number plus two is the same number, then find the number?

  • Last Updated : 03 Sep, 2021
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Number System, any of various sets of symbols and therefore the rules for using them to denote numbers, which are wont to state what percentage objects are there during a given set or in other words Number system is a mathematical presentation of numbers of a given set.

Square Root

The square root of a number is a value, which on multiplication by itself gives the original number.  The symbol used for square root is √, for example, square root of 2 is √2, square root of 4 is √4 which is equal to 2. A number that can be written as the square of another number is called a perfect square. The exact square root of these numbers can be easily calculated using square root.

Linear Equation 

An equation is when two algebraic expressions are equated to each other using an equal “=” sign. An equation with a degree equal to one (the highest power of the variable in the equation is one) is termed a Linear Equation. Linear equations can be formed by the sufficient information given in the questions regarding variables. Let’s take a look at the problem statement,

If the square root of a number plus two is the same number, then find the number?


Let the number be x. According to the question, the square root of a number plus two is the same number.


x1/2 + 2 = x

As the square root is present on one side and one side linear, therefore take square root one side and square it.

x(1/2) = x – 2

To remove the square root, square both sides,

(x(1/2))2 = (x – 2)2

x = x2 + 4 – 4 × x                  (by using (a-b)2 = (a2 + b2 – (2 × a × b)) 


x2 – 5 × x + 4 = 0

As it is a quadratic equation, we will finds its roots 

x2 – 4 × x – x + 4 = 0

x × (x – 4) -1 × (x – 4 ) = 0

(x-4) × (x-1) = 0

x – 4 = 0  which gives x = 4

and x – 1 = 0 which gives x = 1 .

Squared the equation, check both values of x by putting it in our equation to see whether it is correct or not .

By putting x = 4 in the equation,

          4(1/2) + 2 = 4

          2 + 2 = 4

          4 = 4

Therefore, x = 4 satisfies the equation.

By putting x = 1 in the equation,

         1(1/2) + 2 = 1

         1 + 2 = 4

         3 = 4 which is not equal 

Therefore, x = 1 doesn’t satisfies the equation.

Therefore, answer is 4.

Similar Problems

Question 1: Is 361 is a perfect square?


Yes, it is square of 19 i.e. 19 × 19 = 361.

Question 2: Can generalize, the square of any natural number is multiple of any natural number?


Yes, square of any natural number is multiple of 3 or one more than a multiple of 3.

Question 3: State True or False 

“When a polynomial is multiplied by itself, then it is a perfect square.”



Question 4: How many even perfect squares between 1000 and 5000 are divisible by both 5 and 9?


Only one i.e. 3600

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