Square Root of 28
The square root of 28 is approximately 5.291503, or exactly 2√7 in simplified radical form. No, 28 is not a perfect square. Its square root is irrational and never terminates or repeats as a decimal.
Where √28 sits
5² = 25 and 6² = 36, and 28 falls between them, so √28 is between 5 and 6. It's closer to 5 (3 above 25, 8 below 36), which matches the decimal 5.291503.
| k | k² | Compared to 28 |
|---|---|---|
| 3 | 9 | 19 below |
| 4 | 16 | 12 below |
| 5 | 25 | 3 below |
| 6 | 36 | 8 above |
| 7 | 49 | 21 above |
| 8 | 64 | 36 above |
Working it out by hand: Newton's method
Start with a guess (the nearest whole root, 5), divide 28 by it, and average the guess with the result. Each pass roughly doubles the number of correct digits:
| Pass | Guess x | 28 ÷ x | New guess (x + 28÷x) ÷ 2 |
|---|---|---|---|
| 1 | 5 | 5.6 | 5.3 |
| 2 | 5.3 | 5.283019 | 5.291509 |
| 3 | 5.291509 | 5.291496 | 5.291503 |
| 4 | 5.291503 | 5.291503 | 5.291503 |
After 4 passes the guess is 5.291503, already matching √28 = 5.291503 to six decimal places.
Exact form from the prime factors
28 = 2^2 × 7. Each pair of matching primes comes out of the root as one factor, and what's left stays inside: √28 = 2√7. That's the exact value; the decimal 5.291503 is a rounding of it.
Frequently Asked Questions
What is the square root of 28?
The square root of 28 is approximately 5.291503, or exactly 2√7 in simplified radical form.
Is 28 a perfect square?
No, 28 is not a perfect square. Its square root is irrational and never terminates or repeats as a decimal.
What two whole numbers is √28 between?
Between 5 and 6, because 5² = 25 and 6² = 36.
What are the square roots of the numbers right next to 28?
√27 is about 5.1962, and √29 is about 5.3852. 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 √28 squared?
Exactly 28 -- squaring undoes the square root. Squaring the rounded decimal 5.291503 gives 28, which is why the radical form 2√7 is the exact answer and the decimal is an approximation.
What is the negative square root of 28?
−5.291503. Every positive number has two square roots, one positive and one negative, because (−5.291503)² is also 28. The radical sign √ by convention means the positive one.
More Number Theory
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