Square Root of 5 is approximately 2.236 which is an irrational number that can be written as a non-repeating and non-terminating decimal expansion.

Even, the square root of 5 is denoted as √5 and is said to be the positive algebraic number which, if multiplied by itself will give the prime number 5. So, Let’s see the value of the square root of 5, in various methods.

What is the Value of Square Root of 5?

A square root of 5 can be expressed as √5 and √5 is the result of multiplying the number “2.236. . .” by the number itself i.e., number is 2.236 multiplied twice “2.236 × 2.236” then we get the number 5.

A square root of 5 can be written as given below:

√5 = 2.236

OR

(5)^1/2 = 2.236

Square Root of 5 Calculator

To calculate the square root of 5, you can use this basic tool given below:

How to Calculate a Square Root of 5?

Some of the methods are given below to find out the square root of 5.

• Square Root of 5 by Long Division Method
• Square Root of 5 by Estimation Method

Let’s discuss these methods in detail as follows:

Square Root of 5 by Long Division Method

A systematic technique used to figure out the number’s root is necessary only when we have utilized the long division method to compute a number’s square root. In order to calculate the square root of 5 by using the long division method. So, Let’s follow the procedures in a few steps:

• Let’s begin with the number 5.
• Then, Pair the digit after using the decimal point and Find the largest digit whose square is less than 5. Hence that will be 2.
• After that, Subtract the square (4) from the first pair (5).
• Then the remaining number will be 1, which after the decimal point brings down the next pair (00).
• Now, Double the quotient (2) and write a placeholder to get 4.
• The next digit will be 2 to complete the divisor because 42 × 2 = 84.
• After that, Subtract the result (84) from the remaining pair (00). Bring down two zeros.
• Double the existing quotient (2.2) and add a digit to get a new divisor (84).

Therefore, By the long division method you get the approximate value of the square root of 5 is 2.23….. so on.

Square Root 5 by Estimation Method

To get closer to the real value, we first estimate the square root of 5 using the estimation method. Some of the steps are given below;

• Let’s start with 2 because it’s close to the square root of 4.
• Now, Find the average of the guess number and the original number that will be (2 + 5) / 2 = 7 / 2 = 3.5, So the new estimate is 3.5
• Again with the repeating process, (3.5 + 5) / 2 = 8.5 / 2 = 4.25, So the estimate value is 4.25
• Same again, (4.25 + 5) / 2 = 9.25 / 2 = 4.625, The new estimate is 4.625.

Therefore, The square root of 5 is approximately 2.23

Is Square Root of 5 Rational or Irrational?

The square root of 5 is an irrational number. Let’s assume it is in value of √5 that can be expressed in the form of a quotient or division of two integers, i.e. p/q, where q is not equal to 0. Therefore, √5  = 2.23607 and due to its never-ending process after the decimal point that is why it’s an irrational number.

Square Root of 5: FAQs

What is the Square Root Value of 5?

Square root of 5 is approximately equal to 2.23607.

What is a Square of 5?

The square of 5 can be written as 5² and it can be calculated as 5² = 5 × 5 = 25. Therefore, the square of 5 is equal to 25.

Is Root 5 a Rational Number?

No, the square root of 5 (√5) is not a rational number. It is an irrational number, meaning it cannot be expressed as a simple fraction of two integers.

Is 5 a Perfect Square?

No, 5 is not a perfect square because it’s a prime number and cannot be expressed as the product of an integer multiplied by itself.