How to find the square root of 24? What is the square root of 24?

The square root of 24 is 4.898 mentioned with a symbol √. The square root of 24 is denoted using √24 or 24^1/2. In the radical form, the square root of 24 is represented as 2√6.

The square root of a number is determined when a quantity of a number is produced when multiplied by itself or a factor of a number when multiplied by itself gives the original number. In simple terms when a value is multiplied by itself it gives the original number.

For a better understanding,
the number 11 when multiplied by itself (11× 11) = 121. The square root for (121) is 11. 
Square root of 24 = ±2√6
The square root of 24 in decimal form,
√24=  4.898
The square root of 24 in exponent form, 
24^1/2= 4.898

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The calculation for the square root of 24

To find the square root of any number first the given number is usually checked to determine whether they are a perfect square number or not. The square root of the number is found using the long division method.

For the numbers with a perfect square, it is easy to find the square roots and it is a bit tough for non-square values. Numbers like 4,9, 16,25, etc., are perfect squares.

Numbers such as 2,3,7,18,72, and 24 are not perfect square numbers.
24 is not a rational number or a perfect square number. Prime factorization cannot be used to find the square root of 24. Hence, the long division method is used to find the square root of 24.

Methods to find the square root

There are three methods to find the square root of a number

• Prime factorization method
• Long division method
• Repeated subtraction
  These methods described above do not apply to finding the square root of any number.  

Prime factorization method

To find the square root of a number using the prime factorization method first knows the prime factors of the numbers. Let us take n as a prime number, by grouping their squares we get n² now multiplying them we get the square root of the number. 

• Step 1: Find the prime factor for the given number
  24 = 2×2×2×3
• Step 2: Pair similar prime factors.
  24 = 2×22×3
• Step 3: Take square on both sides
  √24=√2√22√3
  You can cancel the square with the square root we get
  √24 = 2×6
• Step 4: Multiply the factors
  The 6 = 2.5 (approximately)
  √24 = 2×2.5
  Hence, √24 = ≈4.9

Long division method

Long division is one of the easiest methods to find the square root of any number. It was the preferred method to be used for the non-perfect square numbers. Find the integer that can divide the number and proceed with the long division. 

Steps to find the square root of 24:

• Step 1: Find the smallest integer that can divide the number. 
• Step 2: Keep following the long division using divisor and dividend. 
• Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number.  

Find the square root of 24

• Step 1: Find the smallest integer that can divide the number. 24 is not a perfect root number and 4 is the nearest number that can divide it. 
• Step 2: Keep following the long division using divisor and dividend. 

Long division method for the square root of 24

• Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number. Hence, the √24 = 4.89

Solved Examples

Example 1: Find the square root of 400 using the prime factorization method.
Solution:
The prime factor of 400 =  2×2×2×2×5×5
By grouping the same prime factor we get 2⁴ 5²

Hence, the square root of 400 is
√400 = 20.

Example 2: What is the square root of 24 using the long division method?
Solution:

The, √24 = 4.89

Example 3: What is the square root of 24 using repeated division
Solution:

• 24 – 1 = 23
• 23 – 3 = 20
• 20 – 5 = 15
• 15 – 7 = 8
• 8 – 9 = -1

The last step in continuous subtraction must be zero and not an integer. Hence, the square root of 18 cannot be found using repeated subtraction methods. 

Example 4: What is an irrational number
Solution:
A number is said to be an irrational number if it cannot be expressed in the form of a ratio or fractions. 
Example: √2, √3, √5 or √24

Example 5: Solve √16×√24
Solution:
The √24 = 4.89
√16 = 4
√16×√24 = 4× 4.89
√16×√24 = 19.56

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