Square Root of 1369 — Value, Simplification, and Steps
Square Root of 1369 — Value, Simplification, and Steps
TL;DR
The square root of 1369 is exactly 37, because 37×37=1369. This article shows why 1369 is a perfect square, works the prime-factorisation and long-division methods, gives a quick-reference table, and points to where 1369 appears.
Last updated on July 18, 2026 | 4 min read
The square root of 1369 is 37. Because 37 is a whole number, 1369 is a perfect square.
Quick Answer:
Result: 1369=37
Notation: whole number, 37
Method shown: prime factorisation and long division
Approximate value: exact — no approximation needed (37.000)
Exact form: 37 (1369 is a perfect square, 37^2 = 1369)
Quick Reference Table
| Expression | Value | Perfect Square? |
|---|---|---|
| 1225 | 35 | Yes (35^2) |
| 1296 | 36 | Yes (36^2) |
| 1369 | 37 | Yes (37^2) |
| 1444 | 38 | Yes (38^2) |
| 1521 | 39 | Yes (39^2) |
| 1369 | 1,874,161 | — |
Where the Square Root of 1369 Appears
1369 is the side length of a square whose area is 1369 square units, so a 37-by-37 grid holds exactly 1369 cells. The number 37 also shows up as a prime that appears in the Pythagorean triple (12, 35, 37).
What a Perfect Square Is
A perfect square is any integer formed by multiplying an integer by itself: 121=11^2, 169=13^2, and here 1369=37^2. Its square root is a whole number with no decimal tail.
Is the Square Root of 1369 Rational or Irrational?
The square root of 1369 is rational. It equals the whole number 37.
How to Compute the Square Root of 1369
Method 1: Prime Factorisation
Break 1369 into primes.
1369=37×37
Take one factor from the pair:
1369=37^2
Final answer: 1369=37.
Method 2: Long Division
Pair the digits from the right: 13∣69. Largest square ≤13 is 9=3^2; first digit 3, remainder 4.
Bring down 69 to make 469; double the 3 to get 6, and find a digit d so that 6d×d≤469. Here 67×7=469 exactly, so the next digit is 7.
Final answer: 1369=37.
Method 3: Estimation
30^2 = 900 and 40^2 = 1600, so 1369 lies between 30 and 40.
Final answer: 1369=37.
Common Mistakes With Square Root of 1369
Mistake 1: Assuming a four-digit number can't be a perfect square
Correct way: confirm 37×37=1369 exactly.
Mistake 2: Mis-pairing digits in long division
Correct way: always pair from the right.
Mistake 3: Halving the number instead of the exponent
Correct way: compute the square root asks what number times itself gives 1369.
Where to Go From Here
To build these skills with a teacher, explore Bhanzu's algebra tutor or help with algebra.
Frequently Asked Questions
Is 1369 a perfect square?
Yes. 1369=37^2.
What is the prime factorisation of 1369?
1369=37^2.
Is the square root of 1369 rational or irrational?
Rational — it is a whole number, 37.
What is the square root of 1444?
38, since 38^2 = 1444.
What is the square root of −1369?
There is no real square root; it is imaginary.