Square Root

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

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### 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 n^{2 }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:**

- 9-1 = 8
- 8-3 = 5
- 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:**

- 15-1 = 14
- 14-3 = 11
- 11-5 = 6
- 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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**FAQs on the square root of 15**

**What is the √15**?

The **√**15 = 3.872

**Which method is used to find the ****√**15?

**√**15

The standard method that is used to find the square root of any number is the long division method.

**How to write the square root of 15 in exponential form?**

(15)^{1/2} or 15^{0.5 }is the exponential way to write ** √**15.

**How to write the square root of 15 in radical form?**

The radical form of writing square root is** √**15.

**Can I find the square root of 15 using other methods?**

Apart from the long division method, prime factorization and repeated subtraction are two methods that are used to find the square root of the number. Repeated subtraction is not applicable to irrational numbers.

**Is ****√**15 an irrational number?

**15 an irrational number?**

**√**Yes, **√**15 is an irrational number since the number is not equal to zero. The square root of 15 cannot be expressed in ratios or fractions.

**What are the methods to find the square root of a number?**

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

Prime factorization method

Long division method

Repeated subtraction

Written by by

Prerit Jain