Square Root of 79
The square root of 79 is approximately 8.888194, or exactly √79 in simplified radical form. No, 79 is not a perfect square. Its square root is irrational and never terminates or repeats as a decimal.
Where √79 sits
8² = 64 and 9² = 81, and 79 falls between them, so √79 is between 8 and 9. It's closer to 9 (15 above 64, 2 below 81), which matches the decimal 8.888194.
| k | k² | Compared to 79 |
|---|---|---|
| 6 | 36 | 43 below |
| 7 | 49 | 30 below |
| 8 | 64 | 15 below |
| 9 | 81 | 2 above |
| 10 | 100 | 21 above |
| 11 | 121 | 42 above |
Working it out by hand: Newton's method
Start with a guess (the nearest whole root, 8), divide 79 by it, and average the guess with the result. Each pass roughly doubles the number of correct digits:
| Pass | Guess x | 79 ÷ x | New guess (x + 79÷x) ÷ 2 |
|---|---|---|---|
| 1 | 8 | 9.875 | 8.9375 |
| 2 | 8.9375 | 8.839161 | 8.88833 |
| 3 | 8.88833 | 8.888058 | 8.888194 |
| 4 | 8.888194 | 8.888194 | 8.888194 |
After 4 passes the guess is 8.888194, already matching √79 = 8.888194 to six decimal places.
Exact form from the prime factors
79 = 79. No prime appears twice, so nothing can be pulled out of the root -- √79 is already in simplest form.
Frequently Asked Questions
What is the square root of 79?
The square root of 79 is approximately 8.888194, or exactly √79 in simplified radical form.
Is 79 a perfect square?
No, 79 is not a perfect square. Its square root is irrational and never terminates or repeats as a decimal.
What two whole numbers is √79 between?
Between 8 and 9, because 8² = 64 and 9² = 81.
What are the square roots of the numbers right next to 79?
√78 is about 8.8318, and √80 is about 8.9443. 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 √79 squared?
Exactly 79 -- squaring undoes the square root. Squaring the rounded decimal 8.888194 gives 79, which is why the radical form √79 is the exact answer and the decimal is an approximation.
What is the negative square root of 79?
−8.888194. Every positive number has two square roots, one positive and one negative, because (−8.888194)² is also 79. The radical sign √ by convention means the positive one.
More Number Theory
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