Square Root

# What is the square root of 17? How to find the square root of 17?

Written by Prerit Jain

Updated on: 25 Aug 2023

Contents

### What is the square root of 17? How to find the square root of 17?

The square root of 17 is 4.123.

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 with a symbol √. The square root of 17 is denoted using √17 or 17^{1/2} . In radical form the square root of 17 is represented as √17.

In simple terms when a value is multiplied by itself it gives the original number. For a better understanding. The number 14 when multiplied by itself (14×14) = 196. The square root for (196) is 14.

**Ways of Writing Square Root**

Square root of 17 =√ 17

Square root of 17 in decimal form,

√17= 4.123

Square root of 17 in exponent form,

17^{1/2}= 4.123

**What is the Square root of 17?**

The square root of a number when multiplied itself gives the original number. The square root of 17 is expressed as √17

√17 = √(Number) × √(Number)

√17 = √(4.123×4.123)

√17 = √(4.123)^{2}

Now, remove the square on the right hand side we get.

√17 = 4.123

Thus, multiplying 4.123 we get the number 17.

**Square root of 17 rational or irrational number**

The number 17 is not a rational number. The square root of 17 is an irrational number.

Why?

A number is said to be rational number if it can be expressed as p/q or q≠0.

The number has a termination point.

For example the number 196 when divided by 14 gives a whole number 14 (196/14 = 14) and it ends there.

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 17 as an example.

The square root of 17 is 4.123 and the number doesn’t end there but continues.

Hence, the number 17 is not a rational number or a perfect square number.

**The calculation for the square root of 17:**

To find the square root of any number first the given number is usually checked to determine whether they are perfect square numbers 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 2,3,7,18,75 and 80 are not perfect square numbers.

17 is not a rational number or a perfect square number. Prime factorization cannot be used to find the square root of 17. Hence, the long division method is used to find the square root of 17.

**Methods to find 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 know 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 17 cannot be found using the prime factorization method. The prime factors of 17 are 1×17. These numbers cannot be simplified further. Hence, the square root of 17 can be found using the 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 17:****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 17**

**Step 1**: Find the smallest integer that can divide the number.

17 is not a perfect root number and 4 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 √ 17 = 4.123

**Solved Examples**

**Example 1: Find the square root of 17 using the repeated subtraction method****Solution:**

17 – 1 = 16

16 – 3 = 13

13-5=8

8-7=1

1-9 = -8

The value in the last step should be zero.

Here, the end value is a negative zero.

Hence, the √17 cannot be found using repeated subtraction methods.**Example 2: what is the square root of 17 using the long division method?****Solution:**

The √17 = 4.123**Example 3: What is the square root of 17 using the prime factorization method****Solution:**

The square root of 17 cannot be found using the prime factorization method. The prime factors of 17 are 1×17. These numbers cannot be simplified further. Hence, the square root of 17 can be found using the long division method.**Example 4: What is an irrational number****Solution:**

A number is said to be an irrational number if it cannot be expressed in the form of ratio or fractions.

Example: √2, √3, √5 or √34**Example 5: Solve 4√17****Solution:**

√17 = 4.123

4√17 = 4×4.123417 = 16.492

**FAQs on the square root of 17?**

**What is the √17**?

The √17 = 4.123

**Which method is used to find the ****√**17?

**√**17

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 17 in exponential form?**

(17)^{1/2} or 17^{0.5 }is the exponential way to write ** √**17

** How to write the square root of 17 in radical form?**

The radical form of writing square root is** √**17

**Can I find the square root of 17 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 or prime factorization is not applicable for irrational numbers.

**Is ****√**17 Is it an irrational number?

**17 Is it an irrational number?**

**√**Yes, ** √**17 is an irrational number since the number is not equal to zero. The square root of 17 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