Square Root Calculator › Square root of 168
Square Root of 168
√168 ≈ 12.961481
168 is not a perfect square, so √168 is an irrational number that is approximately 12.961481. In simplified radical form, √168 = 2√42.
√168 lies between √144 = 12 and √169 = 13.
| Number | 168 |
| Square root (decimal) | 12.961481 |
| Simplified radical | 2√42 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 168
168 = 2^3 × 3 × 7. This is what determines the simplified radical: for √168 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √168 = 2√42.
Estimating √168 by hand
√168 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 168 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 13 |
| Step 2 | 12.961538 |
| Step 3 | 12.961481 |
After 3 steps the estimate is 12.961481, matching √168 ≈ 12.961481.
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Frequently asked questions
Is 168 a perfect square?
No, 168 is not a perfect square, so its square root is irrational and approximately 12.961481.
What is the square root of 168 in simplest radical form?
√168 = 2√42 in simplest radical form.