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Square root of 24
The square root of 24 is a number which when multiplied by itself, results in the number 24. The value of a square root can be a decimal, whole number, and even a negative number. We will now look at how to calculate the square root of 24 and see a few interesting problems.
Square Root of 24: √24 = 4.8989...
Square of 24: 24² = 576
1.  What is the Square Root of 24? 
2.  Is Square Root of 24 Rational or Irrational? 
3.  How to Find the Square Root of 24? 
4.  Important Notes 
5.  FAQs on Square Root of 24 
What is the Square Root of 24?
The square root of a number n is written as √n. It is the inverse operation of squaring a number just like multiplying is the inverse operation to dividing. The square root of 24 can be written in different ways
 Radical form: √24 = 2√6
 Decimal form: 4.89897948...
 Exponent form: (24)^{1}^{/2}
Is Square Root of 24 Rational or Irrational?
 The square root of a perfect square can be expressed as a fraction p/q. However 24 is not a perfect square and its root is, therefore, an irrational number.
 Since the square root of 24 cannot be expressed as p/q, it is an irrational number.
How to Find the Square Root of 24?
We can use 2 methods to find the square root of 24
 Long Division Method
 Prime Factorization Method
One can find out more about the different methods by clicking here
Long Division Method
The square root of 24 by long division method consists of the following steps:
 Step 1: Starting from the left, first pair 24 and place a bar over the digits. We also pair the 0s in decimals in pairs of 2 from left to right.
 Step 2: Find a number that, when multiplied to itself, gives the product less than or equal to 24. The number 4 fits here. Putting the divisor as 4, we get the quotient as 4 and the remainder as 8.
 Step 3: Drag a pair of 0’s down and fill it next to 8 to make the dividend 800.
 Step 4: Double the divisor 4, and enter 8 below with a blank digit on its right. Guess the largest possible digit(X) to fill in the blank and the quotient for which the product of 8X and X results in a value less than or equal to 800. Divide and write the remainder.
 Step 5: Repeat this process to get the decimal places you want.
Prime Factorization Method
The first step in this method is to find the prime factors of 24.
24 = 2 × 2 × 2 × 3
To find the root from here, we can simplify this to
√24 = √(2 × 2 × 2 × 3)
√24 = 2√6
We can either leave it at this or find the root of 6 which is 2.45 and simplify further
Therefore, Square Root of 24 = 2√6 ≅ 4.9
Explore Square roots using illustrations and interactive examples
Important Notes
 There are 2 real roots of 24, 4.899 and 4.899
 There will be n/2 digits in the square root of an even number with n digits.
 There will be (n+2)/2 digits in the square root of an odd number with n digits
Solved Examples

Example 1: Ben wants to fence his square backyard. The backyard has an area of 24 square feet. How long is each side of the backyard?
Solution:
To find the side of the square garden, we will have to find the square root of 24. The square root is √24 = 2√6. Hence, the side length of the garden is 2√6 feet.

Example 2: Mike wants to find out the square root of 124 for a problem he is solving. Help him calculate its value.
Solution:
The square root of 124 can be calculated by following these steps
 √124 = √(2 × 2 × 31)
 √124 = 2 × √31
 √124 = 2√31
Therefore, the square root of 124 is equal to 2√31= 11.135.
FAQs on Square Root of 24
What is the value of √24 times √24?
The value of √24 × √24 = 24
Is 24 a perfect square root?
24 is not a perfect square. 24 is a natural number, but since there is no other natural number that can be squared to result in the number 24, it is NOT a perfect square.
What are the square roots of 24?
The square roots of negative numbers are imaginary.
These are expressed as √24 = +2√6i and 2√6i.
Is the square root of 24 a rational number?
No, the square root of 24 is not a rational number since the square root of 24 is nonterminating and cannot be represented in the form of p/q.
Can we find the square root of 24 by the repeated subtraction method?
No, we can’t find the square root of 24 by repeated subtraction method as it can be used only for perfect squares. 24 is not a perfect square.
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