Square Root of 24

Square root of 24 is 4.8989, The number 24 is produced when you multiply the square root of 24 by itself. Therefore, A square root can have a decimal, whole, or even negative value as its value. Next, we will see some interesting puzzles and see how to find the square root of 24.

Square Root Definition

Square root is the inverse relation to square which help us find the number which multiplied with itself results in the original number for which we have calculated square root.

The square root of is denoted as √x and some examples of square root are:

The square root of 25 is 5 because 5 × 5 = 25. This is denoted as √25 = 5.
The square root of 64 is 8 because 8 × 8 = 64. This is denoted as √64 = 8.
Square root of 22 is an irrational number, approximately 1.41421, because 1.41421×1.41421 ≈ 22.

Value of Square Root of 24

Square Root of 24 is approximately 4.898 as 24 is not perfect square thus it can’t be calculated exactly. √24 is an irrational number and it has non-terminating and non-repeating decimal expansion.

Square Root of 24 is denoted as √24 or (24)^1/2 and can be simplified as 2√6. Thus,

√24 = (24)^1/2 ≈ 4.898

Square Root of 24 Calculator

How to Find the Square Root of 24?

Some of the methods are given below to find out the square root of 24.

Square Root of 24 by Long Division Method
Square Root 24 by Prime Factorization Method

Square Root 24 using the Long Division Method

The following are the steps given below to use the long division method to calculate the square root of 24:

Step 1: Let’s begin with the number 24, and start pairing it from right to left.
Step 2: Choose a perfect square less than 24 as the initial dividend (e.g., 16). Hence divisor will be 4.
Step 3: Since the divisor is 4, the quotient is 4 therefore dividend will be 16. Subtract 16 from 24 and add 4 in the divisor.
Step 4: The new divisor is 8, the dividend is 8. Now put decimal after 4 in quotient and bring down two zeros. Therefore new dividend is 800.
Step 5: Add a digit at the left of 8 in the divisor i.e. at the unit place and also place the same digit in the quotient such that the product is near to 800.
Step 6: Add 8 in the divisor using step 5 hence, the new dividend will be 88 × 8 = 704. Subtract 704 from 800.
Step 7: Continue with this until the square root of 24 is obtained to three decimal places.

Therefore, the value of the square root of 24 approximately will be 4.898… so on.

Read More about Square Root by Long Division Method.

Prime Factorization Method

Let’s derive the square root of 24 in the following steps by using the prime factorization method;

Step 1: Break down 24 into prime factors; 24 = 2 × 2 × 2 × 3.
Step 2: Now make the identical pairs of numbers 24 = (2 × 2) × 2 × 3.
Step 3: After that take a number from each pair and multiply it together. √ 24 = √ (2 × 2) × 2 × 3.
Therefore √ 24 = 2√6.
Step 4: √6 approximate values be 2.449; it will be written as √ 24 = 2 × 2.449 = 4.898
Step 5: Therefore, the square root of 24 is 2√6 or 4.898.

Read More about Prime Factorization.

Is Square Root 24 Rational or Irrational?

24 is an irrational square root. We check to see if the integer under the square root sign (the radicand) is a perfect square in order to establish whether a square root is rational or irrational. So, Here 2³ ×3 is the prime factorization of 24 and 24 is not a perfect square because there isn’t a repeated prime factor.

Therefore 24 is an irrational number since its square root cannot be written as a simple fraction.

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