The square root of 18 is the number when multiplied with itself results in 18. The square root of a number is both positive and negative of the numerical value we obtain using different methods. In this mini-lesson, we will calculate the square root of 18 by prime factorization and long division method along with few interesting problems.

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Square root of 18: √18 = 4.2426Square of 18: 18² = 324
 1 What Is the Square Root of 18? 2 Is Square Root of 18 Rational or Irrational? 3 How to Find the Square Root of 18? 4 Important Notes on Square Root of 18 5 Challenging Questions 6 FAQs on Square Root of 18

## What is The Square Root of 18?

The square root of 18 is written as √18 = 4.2426Square root of 18 in radical form = √18 = √(2 × 3 × 3) = 3√2Hence, 18 is not a perfect square

## Is Square Root of 18 Rational or Irrational?

The square root of 18 is a non-repeating and non-terminating number. Hence, the square root of 18 cannot be represented as a ratio of two integers.

## How to Find the Square Root of 18?

The square of 18 can be evaluated using the prime factorization method or long division method.

### Square Root of 18 by Prime Factorization Method

To find the square root of 18 firstly we will find the prime factorization of 1818 = 2 × 3 × 318 = 2 × 32Now this can be simplified into √18 = √(2 × 32)√18 = √2 × √32√18 = 3√2Therefore, the square root of 18 can be simplified as √18 = 3√2

### Square Root of 18 By Long Division

With the help of the following steps, we can find the square root of 18 via the long division method.

Write 18 as shown in the diagram. Start grouping the digits from the right end by putting a bar on top of them.Now find a number which when multiplied with itself gives a number less than equal to 18. We know that 4 × 4 = 16Find a number for the unit’s place of divisor such that will result in a number less than equal to 200.Bring the next pair of zeros down and repeat the steps till the last pair of zeros.Therefore, we get the square root of √18 = 4.2426 by the long division method.

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Important Notes:

The square root of 18 is represented as √18 in radical form.The square root of 18 is represented as (18)1/2 in exponential form.

Challenging Questions:

Find the value of √√18?Jake initially planned to make a square-shaped pool of area 20 square feet but was only able to make a pool with an area of 18 square feet. By how many feet the side of the pool is short than what was initially planned?

Example 1: Find the square root of 18 using the approximation method?

Solution:For calculating the square root of 18 via the approximation method first we need to find two perfect squares between which 18 lies.We know that 16 and 25 are the two perfect squares between which 18 lies. So, the square root of 18 will be greater than 4 but less than 5. Therefore, the whole number part will be 4.Now for the decimal part, we will use the formula:

Given number- Lower perfect square / Bigger perfect square-Lower perfect square= (18-16)/(25-16)= 2/9= 0.22So, the approx. the square root of 18 will be 4.22

Example 2: Kevin wants to calculate the square root of 7/18. Can you help Kevin?

Solution:Square root of 7 = √7Square root of 18 = 3√2Hence, Square root of 7/18 = √7/(3√2) = 3√(7/2)