How to find the square root of 15? What is the square root of 15?

The square root of 15 is 3.872. The square root of a number is determined when a quantity of a number is produced when multiplied by itself or a factor of a number when multiplied by itself gives the original number. 

The square root is mentioned using the symbol √. The square root of 15 is denoted using √15 or 151/2. In the radical form, the square root of 15 is represented as √15.

In simple terms when a value is multiplied by itself it gives the original number. For a better understanding. The number 5 when multiplied by itself (5×5) = 25. The square root for  (√25) is 5. 

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Different ways of Writing square root of 15

The square root of 15 = √15
The square root of 15 in decimal form,
√15=  3.872
The square root of 15 in exponent form, 
15^1/2= 3.872

The calculation for the square root of 15

To find the square root of any number first the given number is usually checked to determine whether they are a perfect square number or not. The square root of the number is found using the long division method.

For the numbers with a perfect square, it is easy to find the square roots and it is a bit tough for non-square values. Numbers like 4,9, 16,25, etc., are perfect squares. Numbers such as 2,3,7 and 15 are not perfect square numbers.

Methods to find the square root

There are three methods to find the square root of a number

• Prime factorization method
• Long division method
• Repeated subtraction

These methods described above do not apply to finding the square root of any number. 

Prime factorization method

To find the square root of a number using the prime factorization method first knows the prime factors of the numbers. Let us take n as a prime number, by grouping their squares we get n² now multiplying them we get the square root of the number. 

• The square root of 15 cannot be found using the prime factorization method.
• The prime factors of 15 = 1×15.
• The number cannot be simplified further.
• Hence, the √15 can be determined using a long division method. 

Long division method

Long division is one of the easiest methods to find the square root of any number. It was the preferred method to be used for the non-perfect square numbers. Find the integer that can divide the number and proceed with the long division. 

Steps to find the square root of 15:

• Step 1: Find the smallest integer that can divide the number. 
• Step 2: Keep following the long division using divisor and dividend. 
• Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number.  

Find the square root of 15

• Step 1: Find the smallest integer that can divide the number. 15 is not a perfect root number and 3 is the nearest number that can divide it. 
• Step 2: Keep following the long division using divisor and dividend. 

• Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number. Hence, the √15 = 3.872.

Solved Examples

Example 1: Find the square root of 9 using the repeated subtraction method.
Solution:

1. 9-1 = 8
2. 8-3 = 5
3. 5-5 = 0

Here the number zero is obtained in the third step.
Hence, the square root of 9 is
√9 = 3.

Example 2: What is the square root of 15 using the long division method?
Solution:

The √15 = 3.872

Example 3: What is the square root of 15 using repeated division?
Solution:

1. 15-1 = 14
2. 14-3 = 11
3. 11-5 = 6
4.  6-7 = -1

The last step in continuous subtraction must be zero. The square root of 15 cannot be found using repeated subtraction methods. 

Example 4: What is an irrational number?
Solution:
A number is said to be an irrational number if it cannot be expressed as a fractional number.
The number has no termination point.
Let us take the number 15 as an example.
The square root of 15 is 3.872 and the number doesn’t end there but continues.
Hence, the number 15 is not a rational number or a perfect square number. 

Example 5: Solve 9√ 15
Solution:
The √ 15 = 3.872
9√15 = 9×3.872
9√15 = 34.848

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