# Square Root of 3600 — Value & Steps

## TL;DR
The square root of 3600 is exactly 60, because 60×60=3600. This article shows why 3600 is a perfect square, works the prime-factorisation and long-division methods, gives a quick-reference table, and points to where 3600 appears.

**The square root of 3600 is **60****. Because 60 is a whole number, 3600 is a perfect square.

> **Quick Answer:**  
> **Result:** 3600=60  
> **Notation:** whole number, 60  
> **Method shown:** prime factorisation and long division  
> **Approximate value:** exact — no approximation needed (60.000)  
> **Exact form:** 60 (3600 is a perfect square, 60² = 3600)

## Quick Reference Table

| Expression         | Value     | Perfect Square?               |
|--------------------|-----------|-------------------------------|
| 2500                | 50       | Yes (50² = 2500)              |
| 3025                | 55       | Yes (55² = 3025)              |
| 3600                | 60       | Yes (60² = 3600)              |
| 4225                | 65       | Yes (65² = 4225)              |
| 4900                | 70       | Yes (70² = 4900)              |
| 3600²              | 12,960,000| —                             |

## Where the Square Root of 3600 Appears
3600=60 is the side length of a square whose area is 3600 square units, so a 60-by-60 grid holds exactly 3600 cells. The number 3600 is also the count of seconds in one hour, that is 60×60, which is exactly why its square root is a whole number: 3600 was built as 60² by the base-60 timekeeping the Babylonians handed down.

## What a Perfect Square Is
A **perfect square** is any integer formed by multiplying an integer by itself: 900=30², 2500=50², and here 3600=60². Its square root is therefore a whole number with no decimal tail. Because 3600 is a perfect square, \( \sqrt{3600} \) is rational and exact, unlike a root such as [\( \sqrt{78} \)](/content/math/algebra/square-root-of-78/index.html), which never terminates.

## Is the Square Root of 3600 Rational or Irrational?
The square root of 3600 is **rational**. It equals the whole number 60, which can be written as the ratio \( \frac{60}{1} \), so it meets the definition of a rational number. Every perfect square has a rational square root.

## How to Compute the Square Root of 3600
### Method 1: Prime Factorisation

Break 3600 into primes.

\( 3600=36 \times 100 = (2^2 \times 3^2) \times (2^2 \times 5^2) = 2^4 \times 3^2 \times 5^2\)

Take one factor from each pair (each even power halves):

3600=\( 2^2 \times 3 \times 5 = 4 \times 3 \times 5 = 60 \)

**Final answer:** 3600=60.

### Method 2: Long Division

Pair the digits from the right: 36∣00.

Largest square ≤36 is 36=6; first digit 6, remainder 0.

Bring down 00 to make 0; double the 6 to get 12, and the next digit is 0 because 120×0=0.

Remainder 0, so the root is 60.

**Final answer:** 3600=60.

### Method 3: Splitting Off the Trailing Zeros

Write 3600=36×100.

3600=36×100=6×10=60.

**Final answer:** 3600=60.

## Common Mistakes With Square Root of 3600
### **Mistake 1: Halving each trailing zero**
**Where it slips in:** thinking "3600 has two zeros, so drop one and take √36 = 6, giving 6 tens."

**Don't do this:** the shortcut is fine, but only when the digit block is itself a perfect square.

**The correct way:** split as 36×100=6×10=60.

### **Mistake 2: Taking the whole exponent instead of half**
**Where it slips in:** after prime factorisation, multiplying the primes as they stand.

**Don't do this:** write 3600=2⁴×3²×5².

**The correct way:** halve each exponent, giving 60.

### **Mistake 3: Confusing 3600 with 360**
**Where it slips in:** dropping a zero while copying the problem.

**Don't do this:** report 360≈18.97 as if it were 3600.

**The correct way:** 3600=60 exactly; 360 is irrational and roughly 18.974, a completely different number.

## Frequently Asked Questions

**Is 3600 a perfect square?**  
Yes. 3600=60², so its square root is the whole number 60.

**What is the prime factorisation of 3600?**  
3600=2⁴×3²×5², and halving the exponents gives 60.

**Is the square root of 3600 rational or irrational?**  
Rational — in fact a whole number, 60, because 3600 is a perfect square.

**What is the square root of 4900?**  
70, since 70² = 4900, the next multiple-of-ten square above 3600.

**What is the square root of −3600?**  
There is no real square root of a negative number; −3600=60i, where i=√−1 is the imaginary unit.