Square Root of 576 Explained with Simple Method

In Mathematics, the square root of 576 is a value which when multiplied by itself gives the number 576. For example, 24 × 24 = 576. Accordingly, the square root of 576 is 24. Therefore, we can say the value of the square root of 576 is equivalent to 24. It is represented as √576 = 24 in radical form. There are two procedures to find the square root of 576. The two procedures to determine the square root value of 576 are Prime Factorization Method and Long Division Method. In this article, we will discuss both the procedures to find the square root that will help the students to calculate the square root of any numbers speedily and easily.

On the basis of the above equation, we can define that the square root of natural number 576 is 24. Digit 24 is a value which when multiplied by itself gives the result 576.

Hence, 24 × 24  = 576.

What does Square Root Mean?

The square root of a number is another number which obtains the initial number when it is multiplied by itself. For example, 5× 5 = 25. Hence, the value of the square root of 25 is 5.

In Mathematics, the symbol used to denote square root is ‘ √ ’. This symbol of square roots is also known as radical. The number written inside the square root symbol is known as radicand.

Methods to Find Square Root

The two methods to calculate the square root of a given natural number are:

1. Prime Factorization Method

2. Long Division  Method

Prime Factorization Method

In Mathematics, the prime factorization method is a method to calculate the prime factors of a given number. The prime factorization method is simple to use as we have read about the prime factors in our previous classes. The prime factorization method  can only be applied if the number given is a perfect square. A number calculated by squaring a number is known as a perfect square. For example, 16, 25, 576 etc are  perfect squares.

As we know, 576 is a perfect square

\[576=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\]

If we take the square root of both the left and right hand sides, we get

\[\sqrt{576}=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\]

We can see 3 pairs of 2 and 1 pair of 3 in the above given prime factors of 576.

\[\sqrt{576}=2\times 2\times 2\times 3\times 3\]

\[\sqrt{576}=24\]

Hence, the square root of 576 is 24.

Long Division Method

Here, we will discuss the steps to find the square roots of 576 using the long division method.

1. Arrange 576 in pairs of two digits from right to left side.

\[\overline{05}\]    \[ \overline{76} \]

2. We will start with set 1, the largest perfect square less than or equal to 5 is 4 and the square root of 4 is 2. Place the digit  4 at the bottom and 2 at the top as shown in the image below.

  2

\[\overline{05}\]    \[ \overline{76} \]

  4

3. Subtract the digit 4 from the digit 5 and write the difference below. Now, examine the second set of numbers and move the second set of numbers.

   2           

\[\overline{05}\]    \[ \overline{76} \]

   4           

\[\overline{1}\]    \[ \overline{76} \]

4. Find the square of digit 2 which is marked in green at the top. Then use the digit 4 and the number placed at bottom i.e.176  to make the following equation.

4?  × ?  ≤ 176

5. By using the trial and error method, we can find the largest number and fill the blank of the above equation. Replace the question marks in the equation given above with 4 to get:

44 × 4 = 176.

Now, place the digit 4 on top, and 176 at the bottom:

   2   4

 \[\overline{05}\]    \[ \overline{76} \]  

   4              

\[\overline{1}\]    \[ \overline{76} \]            

\[\overline{1}\]    \[ \overline{76} \]

The difference between the bottom two numbers is zero. Hence, we found the answer which is marked in green at the top. The square root of 576 is 24.

Solved Examples

1. Calculate the square root of 256 by using the prime factorization method.

Solution:

Split the number 256 by using the prime factorization method.

(Image will be uploaded soon)

256 can also be written as = 2 × 2 ×2 ×2 × 2 × 2 × 2 × 2.

\[\sqrt{256}= \overline{2\times 2}, \overline{2\times 2}, \overline{2\times 2}, \overline{2\times 2}\]

\[\sqrt{256}= 2\times 2\times 2\times 2\]

\[\sqrt{256}=16\]

2. Find the square root of 900 through the prime factorization method.

Solution:

(Image will be uploaded soon)

900 can be expressed as  = 2 × 2 × 3 × 3 × 5 × 5

\[900=2^{2}\times 3^{2}\times 5^{2}\]

\[\sqrt{900}=\sqrt{2^{2}\times 3^{2}\times 5^{2}}\]

=\[ 2\times 3\times 5 \]

= 30

3. Find the square root of 97344 using the long division method.

Solution:  

(Image will be Uploaded soon)

Hence, the square root of 97344 is 312

\[\sqrt{97354}=312\]

576th Square Root

576 is divided by 24 to get the square root. It is written as 576 = 24 in radical form. There are two ways for calculating the value to root 576 that do not require the use of a calculator: prime factorisation and long division. We'll go over both ways here, which will enable students to discover the root of any number quickly and easily. Also, get a thorough understanding of square roots here.

The square root of 576, as defined by the preceding equation, is a value (i.e. 24) that when multiplied by itself yields 576.

As a result, 24 × 24 = 576 (or 242 = 576).

The Square Root of 576 has been Simplified

We'll learn two distinct approaches to find the square root of 576 without using calculators.

Factorization in the First Place:

We shall write the prime factors of the given number using the prime factorisation method. Finding prime factors of numbers is something we've already learnt in earlier classes. However, this method can only be used to find square roots if the input number is a perfect square.

576 is clearly a perfect square, hence the prime elements are,

\[576=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\]

As a result, we get; if we take the square root on both sides.

\[\sqrt{576}=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\]

There are three pairs of 2 and one pair of 3 as seen above.

Hence,

\[\sqrt{576}=2\times 2\times 2\times 3\times 3\]

\[\sqrt{576}=24\]

Method of Long Division

The long division approach can also be used to obtain the square root of perfect squares. This is the quickest way to get the root of a number, and it's especially handy for imperfect squares and huge integers. The procedures for finding the value of 576 using the long division method are listed below.

• For the division, take the first digit, 5, and leave the remaining two digits, 76.

• The square of 2 is now 4. Using 2 as the divisor, 4 as the quotient, and 5 as the dividend, we get a remainder of 1.

• We'll now deduct the other two numbers, 76 and 2, from the dividend and add 2 to the previous divisor to produce our next divisor, 2+2 =4.

• Because the last digit is 6, either the square of 4 or the square of 6 can be used to get the last digit to be 6.

• As a result, we'll combine 4 with 4 and multiply by 4 to get 176 (44 x 4).

• As a result, the final quotient is 24, which is the correct answer.

The steps to find the root of 576 are listed below.