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Square root of 576
The square root of 576 is the inverse of the mathematical operation of squaring the number 24. The square root of a number implies a number whose product with itself gives the initial number. Now we will calculate the square root of 576 using various methods and a few interesting facts and problems too.
 Square root of 576: 24
 Square of 576: 331776
1.  What Is the Square Root of 576? 
2.  Is Square Root of 576 Rational or Irrational? 
3.  How to Find the Square Root of 576? 
4.  FAQs on Square Root of 576 
5.  Important Notes on Square Root of 576 
What Is the Square Root of 576?
The square root of 576 can be written as √576 and (576)^{1/2}
The square of 576 will be a number(a) such that a × a = 576
And 24 × 24 = 576 also 24 × 24 = 576
Therefore, +24 and 24 are the square root of 576
Is Square Root of 576 Rational or Irrational?
The square root of 576 are +24 and 24.
Both numbers are integers and we know that all integers are rational numbers.
Hence, the square root of 576 is a rational number.
How to Find the Square Root of 576?
Now we will find the square root of 576 using different methods.
Square Root of 576 Using Repeated Subtraction Method
Sr. No. 
Subtraction 
Sr. No. 
Subtraction 
1. 
576  1 = 575 
13. 
432  25 = 407 
2. 
575  3 = 572 
14. 
407  27 = 380 
3. 
572  5 = 567 
15. 
380  29 = 351 
4. 
567  7 = 560 
16. 
351  31 = 320 
5. 
560  9 = 551 
17. 
320  33 = 287 
6. 
551  11 = 540 
18. 
287  35 = 252 
7. 
540  13 = 527 
19. 
252  37 = 215 
8. 
527  15 = 512 
20. 
215 – 39 = 176 
9. 
512  17 = 495 
21. 
176  41 = 135 
10. 
495  19 = 476 
22. 
135  43 = 92 
11. 
476  21 = 455 
23. 
92  45 = 47 
12. 
455  23 = 432 
24. 
47  47 = 0 
We have to subtract 24 consecutive times. So, the square root of 576 is 24.
Square Root of 576 by Long Division
We will now find the square root of 576 by the long division method using the following steps.
 Start pairing the digits from the unit’s place in pairs of two digits by putting a bar on top of them. We have two pairs in this case, 5 and 76.
 Find a number(n) such that n × n ≤ 5. So, n will be 2 as 2 × 2 = 4.
 We get the remainder 1 and the quotient 2. Also, add the divisor n with itself to get the new divisor. The new divisor here will be 4.
 Bring down the pair of 96. So, the new dividend is 176.
 Find a number(m) such that 4m × m ≤ 176. So, we get n = 4 as 44 × 4 = 176.
So, we get the square root of √576 = 24 by the long division method.
Explore square roots using illustrations and interactive examples.
Challenging Questions
 Find the square root of the first three multiples of 576.
 By what number 576 should be divided to make it a perfect cube?
Important Notes:
 The number 576 is a perfect square.
 The square root of 576 is a rational number.
 The square root of 576 is an imaginary number.
Square Root of 576 Solved Examples

Example 1: Samuel wants to find the square root of 576 by the prime factorization method. Can you help Samuel?
Solution:
Prime factorization of 576: 2^{6} × 3^{2}
Prime factors of 576 in pairs: (2 × 2) × (2 × 2) × (2 × 2) × (3 × 3)
Square root of 576: √((2 × 2)^{3} × (3 × 3)) = (2)^{3 }× 3 = ±24
Therefore, √576 = ±24

Example 2: Greg wants to know the value of √√576. Can you help Greg to find it out?
Solution:
The Square root of 576 is √576 = 24
Now the prime factorization of 24 = 2^{3} × 3
The square root 24 is (24)^{1/2} = ((2)^{3} × 3)^{1/2} = 2 × (2 × 3)^{1/2} = 2√6 
Example 3: A squareshaped construction site with an area of 576 square yards wants to build a road around the facility such that they have 484 square yards area left for construction. What will be the width of the road?
Solution:
The initial area of the construction site = 576
Length of one side of site = √576 = 24 yards
The final area of the site available for construction = 484
So, the length of one side of the area available for construction = √484 = 22 yards
Therefore, the width of the road around the construction area = 24 – 22 = 2 yards.
FAQs on Square Root of 576
What is the square root of 576 in prime factorization form?
The square root of 576 is √576 = 24.
Now, the prime factorization of 24 = 2 × 2 × 2 × 3
Can we find the square root of 576 using the approximation method?
No, we can’t find the square root of 576 using the approximation method.
576 is a perfect square and this method cannot be used in the case if the given number is a perfect square.
What is the square root of 576?
The square root of negative numbers is imaginary as squares of both positive and negative numbers will result in positive numbers.
The square root of 576 is represented as ±24i.
What is the prime factorization of 576?
Prime factorization of 576: 2^{6} × 3^{2}
How is the square root of 576 is expressed in exponential and radical form?
 The square root of 576 is written as (576)^{1/2} in exponential form.
 The square root of 576 is written as √576 in radical form.
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