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.
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: 26 × 32
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.