Square Root of 62
The square root of 62 is approximately 7.874008, or exactly √62 in simplified radical form. No, 62 is not a perfect square. Its square root is irrational and never terminates or repeats as a decimal.
Where √62 sits
7² = 49 and 8² = 64, and 62 falls between them, so √62 is between 7 and 8. It's closer to 8 (13 above 49, 2 below 64), which matches the decimal 7.874008.
| k | k² | Compared to 62 |
|---|---|---|
| 5 | 25 | 37 below |
| 6 | 36 | 26 below |
| 7 | 49 | 13 below |
| 8 | 64 | 2 above |
| 9 | 81 | 19 above |
| 10 | 100 | 38 above |
Working it out by hand: Newton's method
Start with a guess (the nearest whole root, 7), divide 62 by it, and average the guess with the result. Each pass roughly doubles the number of correct digits:
| Pass | Guess x | 62 ÷ x | New guess (x + 62÷x) ÷ 2 |
|---|---|---|---|
| 1 | 7 | 8.857143 | 7.928571 |
| 2 | 7.928571 | 7.81982 | 7.874196 |
| 3 | 7.874196 | 7.87382 | 7.874008 |
| 4 | 7.874008 | 7.874008 | 7.874008 |
After 4 passes the guess is 7.874008, already matching √62 = 7.874008 to six decimal places.
Exact form from the prime factors
62 = 2 × 31. No prime appears twice, so nothing can be pulled out of the root -- √62 is already in simplest form.
Frequently Asked Questions
What is the square root of 62?
The square root of 62 is approximately 7.874008, or exactly √62 in simplified radical form.
Is 62 a perfect square?
No, 62 is not a perfect square. Its square root is irrational and never terminates or repeats as a decimal.
What two whole numbers is √62 between?
Between 7 and 8, because 7² = 49 and 8² = 64.
What are the square roots of the numbers right next to 62?
√61 is about 7.8102, and √63 is about 7.9373. 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 √62 squared?
Exactly 62 -- squaring undoes the square root. Squaring the rounded decimal 7.874008 gives 62, which is why the radical form √62 is the exact answer and the decimal is an approximation.
What is the negative square root of 62?
−7.874008. Every positive number has two square roots, one positive and one negative, because (−7.874008)² is also 62. The radical sign √ by convention means the positive one.
More Number Theory
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