About Square Root of 576
What is Square Root of 576?
The square root of a number is a number that is multiplied by itself to obtain the given number. For example when a number x is multiplied by itself we get a number y, so we can say that y is a square of x or x is a square root of y.
It is denoted by \( \sqrt{~~} \) a symbol called the radical.
Mathematically, \( \sqrt{y}=x \) (square root of y is x)
Here we have a number 576 whose square root is 24, so we can write it as
\( \sqrt{576}=24 \).
Square Root of 576
We will calculate the square root of 576 by prime factorization method:
Step 1: Find the prime factors of 576
576 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3
Step 2: Make pairs of identical factors.
576 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3
Step 3: Take a factor from each pair and multiply them to get the square root.
\( \sqrt{576} \) = 2 x 2 x 2 x 3
\( \sqrt{576} \) = 24
So, the square root of 576 is 24.
Negative Square Root of 576
Each positive number has two square roots, one is positive and the other is negative, as both the positive and negative numbers have the same absolute value.
Let us understand this with an example:
(-24) \( \times \) (-24) = 576 [Since, multiplying two negatives results in a positive]
Also, multiply 24 by itself
24 \( \times \) 24 = 576
From this calculation, the square of -24 is 576 and the square of 24 is also 576, so we can say that square roots of 576 are both 24 and -24.
Hence, \( \sqrt{576}=\pm 24 \)
In general, \( \sqrt{y}=\pm x \)
Solved Square Root of 576 Examples
Example 1: A square shaped green board has an area 576 square inches. Find the edge length of the board.
Solution:
The board is square in shape, use the area of square formula to find edge length.
A = side\( ^2 \) Write the formula for area of square
576 = side\( ^2 \) Substitute 576 for A
\( \sqrt{576}=\sqrt{\text{side}^2} \) Take square root of each side
\( \pm \)24 = side
We know that length cannot be negative.
So, the edge length of the green board is 24 inches.
Example 2: Evaluate \( (3\sqrt{576}\times 4)+(\sqrt{576}\times 2) \) .
Solution:
\( (3\sqrt{576}\times 4)+(\sqrt{576}\times 2) \) Write the equation
= (3 \( \times \) 24 \( \times \) 4) + (24 \( \times \) 2) Substitute 24 for \( \sqrt{576} \)
= 288 + 48 Multiply
= 336 Add
So, \( (3\sqrt{576}\times 4)+(\sqrt{576}\times 2)=336 \).
Example 3: The area of a baseball field is found to be 1808.64 square feet. Calculate the radius of the ground. (Assume the cricket ground is circular in shape)
Solution:
A = \( \pi \)r\( ^2 \) Write the formula for area of circle
1808.64 = 3.14 \( \times \) r\( ^2 \) Substitute 1808.64 for A and 3.14 for \( \pi \).
576 = r\( ^2 \) Divide by 3.14 on each side
\( \sqrt{576}=\sqrt{r^2} \) Take positive square root of each side
24 = r Simplify
So, the radius of the cricket ground is 24 feet.
There are two square roots of 576 that are 24 and -24.
The value of minus square root of 576 is -24.
The value of the square root of 576 is 24, which is an integer. Hence, 576 is a perfect square number.
We know that the square root of an even number is even and that of an odd number is odd. Here 576 is an even number, so the square root of 576 is an even number.
A number whose square root is an integer is known as a perfect square number.