Square Root of 44
The square root of 44 is approximately 6.63325, or exactly 2√11 in simplified radical form. No, 44 is not a perfect square. Its square root is irrational and never terminates or repeats as a decimal.
Where √44 sits
6² = 36 and 7² = 49, and 44 falls between them, so √44 is between 6 and 7. It's closer to 7 (8 above 36, 5 below 49), which matches the decimal 6.63325.
| k | k² | Compared to 44 |
|---|---|---|
| 4 | 16 | 28 below |
| 5 | 25 | 19 below |
| 6 | 36 | 8 below |
| 7 | 49 | 5 above |
| 8 | 64 | 20 above |
| 9 | 81 | 37 above |
Working it out by hand: Newton's method
Start with a guess (the nearest whole root, 6), divide 44 by it, and average the guess with the result. Each pass roughly doubles the number of correct digits:
| Pass | Guess x | 44 ÷ x | New guess (x + 44÷x) ÷ 2 |
|---|---|---|---|
| 1 | 6 | 7.333333 | 6.666667 |
| 2 | 6.666667 | 6.6 | 6.633333 |
| 3 | 6.633333 | 6.633166 | 6.63325 |
| 4 | 6.63325 | 6.63325 | 6.63325 |
After 4 passes the guess is 6.63325, already matching √44 = 6.63325 to six decimal places.
Exact form from the prime factors
44 = 2^2 × 11. Each pair of matching primes comes out of the root as one factor, and what's left stays inside: √44 = 2√11. That's the exact value; the decimal 6.63325 is a rounding of it.
Frequently Asked Questions
What is the square root of 44?
The square root of 44 is approximately 6.63325, or exactly 2√11 in simplified radical form.
Is 44 a perfect square?
No, 44 is not a perfect square. Its square root is irrational and never terminates or repeats as a decimal.
What two whole numbers is √44 between?
Between 6 and 7, because 6² = 36 and 7² = 49.
What are the square roots of the numbers right next to 44?
√43 is about 6.5574, and √45 is about 6.7082. Square roots increase more slowly as the number gets bigger, which is why consecutive whole numbers have roots that get closer together the higher you go.
What is √44 squared?
Exactly 44 -- squaring undoes the square root. Squaring the rounded decimal 6.63325 gives 44, which is why the radical form 2√11 is the exact answer and the decimal is an approximation.
What is the negative square root of 44?
−6.63325. Every positive number has two square roots, one positive and one negative, because (−6.63325)² is also 44. The radical sign √ by convention means the positive one.
More Number Theory
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