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Square Root of 5
The square root of 5 is expressed as √5 in the radical form and as (5)^{½} or (5)^{0.5} in the exponent form. The square root of 5 rounded up to 5 decimal places is 2.23607. It is the positive solution of the equation x^{2} = 5.
 Square Root of 5: 2.23606797749979
 Square Root of 5 in exponential form: (5)^{½} or (5)^{0.5}
 Square Root of 5 in radical form: √5
What Is the Square Root of 5?
Let us first understand the meaning of square root. The square root of a number is the number which, when multiplied to itself, gives the product as the original number. Consider the example:
 5^{2} = 5 × 5 is 25
Here 5 is called the square root of 25. 25 is a perfect square. So the square root of 25 is 5. Now, what is the square root of 5? Does that mean nonsquare numbers cannot have a square root? Nonsquare numbers also have a square root, just that they are not whole numbers. For real numbers a and b,
 a^{2}=b is a=√b
The square root of 5 in the radical form is expressed as √5 and in exponent form, it is expressed as 5½. The square root of 25 is the inverse operation of squaring 5 and 5
 5 × 5=25
 (5) × (5) = 25.
Let us look at the square root of 5
Square Root of 5
We know that factors of 5 are 5 × 1 = 5
 √5 = 2.23
 5 is not a perfect square.
Is the Square Root of 5 Rational or Irrational?
A number that can be expressed as a ratio of two integers, that is, p/q, q ≠ 0 is called a rational number. Now let us look at the square root of 25. √25 = 5 = 5/1. Thus, √25 is a rational number. Now let us look at the square root of 5
 √5 = 2.23
A number that cannot be expressed as a ratio of two integers is called an irrational number.
 5 is not a perfect square.
 The square root of 5 is an irrational number.
How to Find the Square Root of 5?
There are different methods to find the square root of 5. The first method is by prime factorization and the second is the conventional long division method.
Square Root of 5 Using Prime Factorization
Let us find the square root of 5 using prime factorization:
 5 = 5 × 1
 5 = 5
Taking square root
 √5 = √5
 √5 = 2.23
Let us now try finding the square root of 5 by the long division method.
Square Root of 5 By Long Division
Let us follow these steps to find the square root of 5 by the long division method.
 Step 1: Group the digits into pairs (for digits to the left of the decimal point, pair them from right to left) by placing a bar over them. Since our number is 5, let us represent it inside the division symbol.
 Step 2: Find the largest number such that when you multiply it with itself, the product is less than or equal to 5. We know that 2 × 2 is 4 and is less than 5. Now let us divide 5 by 2
 Step 3: Let us place a decimal point and pairs of zeros and continue our division. Now, multiply the quotient by 2 and the product becomes the starting digit of our next divisor.
 Step 4: Choose a number in the unit's place for the new divisor such that its product with a number is less than or equal to 100. We know that 2 is in the ten's place and our product has to be 100 and the closest multiplication is 42 × 2 = 84
 Step 5: Bring down the next pair of zeros and multiply the quotient 22 (ignore the decimal) by 2, which is 44 and the starting digit of the new divisor.
 Step 6: Choose the largest digit in the unit's place for the new divisor such that the product of the new divisor with the digit at one's place is less than or equal to 1600. We see that 443, when multiplied by 3, gives 1329 which is less than 1600. Our long division now looks like
 Step 7: Add more pairs of zeros and repeat the process of finding the new divisor and product as in step 2
Note that the square root of 5 is an irrational number, i.e, it is neverending. So, stop the process after 4 or 5 iterations, and you have the square root of 5 by the long division method.
Explore Square roots using illustrations and interactive examples
Challenging Questions:

Evaluate the following:
a) 5√25 + 5√4 + 5√16
b) 5√5 + 7√5  10√5
c) 5√6 + 5√25  5
Important Notes:
 The square root of 5 in the radical form is expressed as √5.
 In exponent form, the square root of 5 is expressed as 5^{½}.
Square Root of 5 Solved Examples

Example 1: The area of a square shaped bed is 25m^{2}. Help Alex find the side length of the bed.
Solution
Area of a square = side × side = side^{2}
√25 = Side = 5
The side length of the bed is 5m. 
Example 2: How will Joe prove that square root of 5 is an irrational number and square root of 25 is a rational number?
Solution
The square root of 5 on long division gives value, √5 = 2.23(approximately). While on the other hand if Joe finds square root of 25 using long division, he will follow the below given process:
 Make a pair of digits of 25 starting with a digit at one's place. Put a bar on each pair. Now we have to multiply a number by itself such that the product is less than or equal to 25. Here, 5 × 5 = 25 ≤ 25 so the divisor is 5 and quotient is 5. Now do the division and get the remainder as 0.
 Square root of 25 is 5 (√25 = 5).

Example 3
If the side of a square shape wall clock is 2.33m. What is the area of a square shaps wall clock? Round the answer to the nearest whole number.
Solution
One side of square shape wall clock = 2.23m
Area of square = side^{2}
Area of a square shape wall clock = (2.23)^{2} = 4.9729 = 5m^{2}
FAQs on the Square Root of 5
What is the Value of the Square Root of 5?
The square root of 5 is 2.23606.
Why is the Square Root of 5 an Irrational Number?
The number 5 is prime. This implies that the number 5 is pairless and is not in the power of 2. Therefore, the square root of 5 is irrational.
What is the Square Root of 5?
The square root of 5 is an imaginary number. It can be written as √5 = √1 × √5 = i √5 = 2.236i
where i = √1 and it is called the imaginary unit.
What is the Square Root of 5 in Simplest Radical Form?
The number 5 is a prime number. This implies that the number 5 is pairless and is not in the power of 2. Therefore, the radical form of square root of 5 cannot be simplified further.
What is the Value of 3 square root 5?
The square root of 5 is 2.236. Therefore, 3 √5 = 3 × 2.236 = 6.708.
Evaluate 12 plus 15 square root 5
The given expression is 12 + 15 √5. We know that the square root of 5 is 2.236. Therefore, 12 + 15 √5 = 12 + 15 × 2.236 = 12 + 33.541 = 45.541
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