Square root of 40
√40 ≈ 6.3246. The square root of 40 is about 6.3246, which simplifies to 2√10. 40 is not a perfect square, so √40 is irrational: its decimals never end or repeat.
| Value | 6.32455532 |
|---|---|
| Rounded | 6.3 (1 dp) · 6.32 (2 dp) · 6.325 (3 dp) |
| Simplest radical form | 2√10 |
| Perfect square? | No — between 6² = 36 and 7² = 49 |
| 40 squared | 1,600 |
Estimating √40 in your head
Start from the nearest perfect square, 6² = 36. 40 is 4 more than that. Divide the difference by twice the root, 12, and add it:
√40 ≈ 6 + 4 ÷ 12 ≈ 6.333
The true value is 6.3246, so the one-step estimate is off by about 0.009. The estimate always comes out slightly high, and it is closest when 40 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √40
Find the largest perfect square that divides 40: it is 4, since 40 = 4 × 10. Take its root outside: √40 = √4 × √10 = 2√10.
Frequently asked questions
What is the square root of 40?
The square root of 40 is about 6.3246, which simplifies to 2√10. 40 is not a perfect square, so √40 is irrational: its decimals never end or repeat.
Is 40 a perfect square?
No. It lies between 6² = 36 and 7² = 49.
What is √40 in simplest radical form?
√40 = √(4 × 10) = 2√10.
Practise estimating square rootsNearby: √39 · √41 · all square roots to 150