Square Root of 18

Square Root of 18 is 4.242640688. In radical form square root of 18 is equal to 3√2. It is represented as either √(18) or (18)^1/2. The square root of a number is a unique number that gives the original number on multiplication with itself.

In this article, we will learn about the value of the square root of 18 and also learn how to find the value of the square root of 18.

Value of Square Root of 18

The square root of 18 is approximately 4.242640687119285. . . or in the radical form, we can write 3√2. Square root of any number is a number which gives the original number when multiplied by itself; in the case of 18, 3√2 × 3√2 = 9 × 2 = 18.

Square root of 18 is an irrational number as it is written as the product of 3 (rational number) and √2 i.e.,3 × √2

Note: As the Square root of 18 is not an perfect square so we don’t get the exact value of square root of 18 from prime factorization method. In case of 18, We use Long Division method to find the

Square Root of 18 Calculator

Try the following calculator to find the value of Square root of 18:

How to Find Square Root of 18?

The Square root of the number is a special number which gives the original number on multiplication with itself. To find Square root of a perfect Square number is quite easy in terms of a non-perfect square.

For example, 4, 9, 25, 36, 49, etc. It is easier to compute the square root as they are perfect square number.

As 18 is a not a perfect square, So to find the root, We usually apply three method:

• Long Division Method

• Prime Factorization Method

Square Root of 18 by Long Division Method

Long division method is the best way to find root of a non-perfect square number. Because It always gives exact value.

Here’s is the step by step explanation of the method:

Step 1: Write 18 as 18.000000 to make it easier to divide

Step 2: Get the largest number whose square is less than or equal to the number in the leftmost group, i.e. 18. We know that 4² < 18 < 5², so we can consider 4. Now, we got 4 as the quotient and 2 as the remainder.

Step 3: We will place a decimal in the quotient and bring down the pair of zeroes for further division.

Step 4: Now add the quotient with the existing divisor, this will become the digit at the tens place for our next divisor.

Step 5: For the unit’s place, we need to find a value that can be placed at the unit place of both quotient and the divisor such that the new divisor when multiplied with the unit digit of the quotient results in the highest number less than the remainder.

Step 6: Again, bring down the next pair 00 and add the divisor with the quotient and enter it on its right as we did previously. We can repeat this process as many times as required.

We can compute the result up to how many decimal places we want or find upto three places and round it of to two places as that can be used for approx. value of the Square root.

Following illustration shows the process of calculating Square Root of 18 using long division.

Read More about Long Division Method.

Square Root of 18 by Prime Factorization Method

This method is more useful when the number is a perfect square. If number is not a perfect square then we don’t get a exact value. we need to multiply with the radical number.

As written above, Square root of 18 in radical form = 3√2. As we know, The value of √2 is 1.414. We are going to use this value to get exact value.

To find the square root of a number using the prime factorization method, follow these steps:

Step 1: we need to break down the given number into prime factors.

Step 2: We need to pair the every prime factors and also ensuring that the factors of each pair is same.

Step 3: Select one factor from each pair.

Step 4: Multiply those factor.

Step 5: The result of multiplication result as square root of number.

Read More about Prime Factorization

The following illustration is given for the prime factorization of 18.

In this prime factorization, we get 1 pair and 1 single number which are {(3 , 3) , (2)}. As discussed in step, We need to choose a factor in every pair. In case of 3, Simply choose 3. But In case of 2, As we know, √2 × √2 = 2. So we make a pair which is {(√2 , √2)}.

So We pick 1 factor with both pair and multiply, 3 × √2. After multiplying, We get Square root of 18 is equal to 4.2427.

Read More,

• Square root of a number
• List of Square Roots from 1 to 30
• Is 18 a whole number?

Square Root of 18: FAQ’s

What is the Simplest Form of √18?

The simplest form of √18 is 3√2.

What is Square of 18?

The square of 18 is 324.

How to Find Square Root of 18?

To find the square root of 18 in its simplest radical form:

• Factor 18 into its prime factors: 18 = 2 × 3²
• Express 18 as a product of squares: 18 = 2 × (3²)
• Apply the square root to both factors: √18 = √(2 × 3²)
• Simplify the square root of the square: √18 = √2 × 3
• The simplest radical form is 3√2

Therefore, the square root of 18 is 3√2

Is 18 a Perfect Cube?

No, 18 is not a perfect cube.

What is Square Root of 18 in Radical Form?

The square root of 18 in radical form is √18 or, simplified, 3√2.