What is Square Root 24?
Finding the square and square root of a number are inverse operations. To find the square of a number you need to multiply the number by itself.
For example: To find the square of a number 5, we will multiply the number by itself, that is,
5 × 5 = 25
Similarly, to find the square root of 25, we will do the inverse operation. A square root is represented by this radical symbol,‘√’.
Since, \(5^2\) = 25
\(\Rightarrow \sqrt{25}\) = 5
On the same lines, the square root of 24 = \(\sqrt{24}\) = \(2\sqrt{6}\).
Deriving the Square Root with Prime Factorization
Steps to calculate the square root of 24 by prime factorization method:
Step 1: Find the prime factors of 24
∴ 24 = 2 × 2 × 2 × 3
Step 2: Make pairs of identical numbers.
24 = (2 × 2) × 2 × 3
Step 3: Take a number from each pair and multiply to get square root.
\(\sqrt{24}\) = \(\sqrt{(2\times2)\times2\times3}\)
\(\sqrt{24}\) = \(2\sqrt{6}\)
Since the value of \(\sqrt{6}\) = 2.449 (approx.)
\(\sqrt{24}\) = 2 × 2.449 = 4.898
So, the square root of 24 is \(2\sqrt{6}\) or 4.898.
Deriving the Square Root by Long Division Method
Steps to find the square root of 24 using the long division method are given as follows:
Step 1: Write the number as shown below by putting the bar on the top of the number;
\(\overline{24}\).\(\overline{00}\) \(\overline{00}\) \(\overline{00}\)
Step 2: By hit and trial method, divide the number 24 by a number, such that the product of the same number should be less than or equal to 24.
So 4 \(\times\) 4 = 16, this is less than 24.
Here, Quotient = 4 and Remainder = 8.
Step 3: Bring down 00 and write it after 8, so the new dividend obtained is 800. Then double the quotient value, so we get 8 in the divisor place.
Step 4: Again by hit and trial method, find the number such that when we multiply it to divisor we get the number less than 800.
88 \(\times\) 8 = 704 < 800
We get the number 8 which when we multiply to 88 we have got 704 which on subtraction with 800 will get us the remainder 96.
Here, Quotient = 4.8 and Remainder = 96
Step 5: Repeat the previous two steps to obtain the quotient up to three decimal places.
Therefore, the value of the square root of 24, that is, \(\sqrt{24}\) is 4.898.
Definition of Negative Square Root
Each positive number has two square roots, one is positive and other is negative as their absolute value is the same.
Let us understand this with example,
\(2\sqrt{6} \times 2\sqrt{6}\) = 24
\(-2\sqrt{6} \times -2\sqrt{6}\) = 24 [Since, (-)\(\times\)(-) = (+)]
From the above, the square of \(-2\sqrt{6}\) is 24 and square of \(2\sqrt{6}\) is also 24. So, we can say that square roots of 24 are \(2\sqrt{6}\) and \(-2\sqrt{6}\) both.
\(\Rightarrow \sqrt{24}\) = ± \(2\sqrt{6}\)
In general,
Rapid Recall
Solved Square Root of 24 Examples
Example 1: The area of a circular crop field is 24\(\pi \text{ft}^2\). Find the radius of the field.
Solution:
Let the radius of the circular crop field is ‘r’ ft.
The area of a field = \(\pi r^2\)
24\(\pi\) = \(\pi r^2\) [Given area = 24\(\pi \text{ft}^2\).]
24 = \(r^2\) [Taking square root on both sides]
\(\sqrt{24}\) = r
∴ 4.898 = r
Therefore, the radius of the circular field is 4.898 ft.
Example 2: Find the value of 8 multiplied by \(\sqrt{24}\).
Solution:
8 × \(\sqrt{24}\)
Since the value of \(\sqrt{24}\) = 4.898
8 × \(\sqrt{24}\) = 8 × 4.898 [Multiply]
= 39.184
Hence, the value of 8 multiplied by \(\sqrt{24}\) is 39.184.
Example 3: Find the value of \((3\sqrt{24}\times \sqrt{6})-(\sqrt{24}\times 2\sqrt{6})\).
Solution:
Given expression: \((3\sqrt{24}\times \sqrt{6})-(\sqrt{24}\times 2\sqrt{6})\)
\((3\sqrt{24}\times \sqrt{6})-(\sqrt{24}\times 2\sqrt{6})\) = \((3 \times 2\sqrt{6} \times \sqrt{6})-(2\sqrt{6} \times 2\sqrt{6})\) [By PEMDAS rule]
= \((6 \times \sqrt{6^2})-(4 \times \sqrt{6^2})\) [Simplify]
= (6 × 6) – (4 × 6)
= 36 – 24
= 12
Therefore, the value of given expression is \((3\sqrt{24}\times \sqrt{6})-(\sqrt{24}\times 2\sqrt{6})\) is 12.
24 has two square roots.
No, 24 is not a perfect square, as the square root of 24 is 4.898 which is in the decimal form.
The square root of 24 is = 4.8989794855..
So, the square root 24 is an irrational number because it is a non-terminating and non-repeating value.