Square Root of 324

In Mathematics, the square root of 324 is defined as a number, which on multiplication by itself for two times, results in the original number 324. The value of the square root of 324 is a rational number since it can be represented in the form of p/q. In this article, we will learn two different such as the long division method and the prime factorization method to determine the square root of 324 with complete explanation.

What is the Value of Square Root of 324?

If a number is multiplied by itself and gives the result as 324, then we can say that the number is the square root 324. Symbolically, the square root of 324 is expressed as √324, which is the radical form of square root of 324.

Hence, √324 = √(Number × Number)

Hence, by multiplying the number 18 for two times, we get the original number 324.

(i.e) √324 = √(18× 18)

√324 = √(18)²

On removing square and square root, we will get

√324 = ± 18

Square Root of 324 by Prime Factorization Method

The square root of 324 can be found using the prime factorization method. To find the value, we should know the prime factorization of 324. Thus, the prime factorization of a number 324 is 2² × 3⁴.

Thus, √324 = (√2)² × (√3)² × (√3)²

√324 = 2× 3× 3

√324 = 18

Hence, the square root of 324 is equal to 18.

Square Root of 324 by Long Division Method

The steps to obtain the square root of 324 using the long division method is provided as follows:

Step 1: First, write the number 324. Next, Pair the number 324 by putting the bar on the top of the number from right to left.

Step 2: Next, divide a number 8 by a number, such that the multiplication of the same number must be less than or equal to 8. Hence, 2×2=4, which is smaller than 8. Thus, we get quotient = 2 and remainder = 4.

Step 3: Double the quotient value, therefore we get 4 and let us take 40 as the new divisor. Now, bring down the number 41 for the division process. Thus, the new dividend obtained is 441. Now, determine the number, such that (40 + new number) × new number will give the product that should be smaller than or equal to 441. Hence, (40+9) × 9 = 441, which is equal to 441.

Step 4: Subtract 441 from 441, and we get 00 as the new reminder, and 18 as a quotient.

Step 5: Thus, the value of the square root of 324, √324 is 18.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify: (4√324)/18.

Solution:

Given: (4√324)/18.

As we know that the square root of 324 is 18.

Substituting the value in the expression,

(4√324)/18 = [4(18)]/18

(4√324)/18 = 4

Therefore, the simplification of (4√324)/18 is 4.

Example 2:

Compute the value of m, if m√324 + 10 = 28

Solution:

Given: m√324 + 10 = 28 …(1)

We know that √324 = 18

Now, substitute the value in equation (1), we get

m(18) + 10 = 28

18m = 28 – 10

18m = 18

m = 18/18 = 1.

Therefore, the value of m is 1.

Example 3:

Simplify (√324 × 10√324) + 28

Solution:

Given expression: (√324 × 10√324) + 28

(√324 × 10√324) + 28 = [10(√324)²] +28

On removing square and square root, we get

(√324 × 10√324) + 28 = [10(324)] + 28

(√324 × 10√324) + 28 = 3240 + 28

(√324 × 10√324) + 28 = 3268.

Hence, the simplified form of (√324 × 10√324) + 28 is 3268.