Square root of 7
√7 ≈ 2.6458. The square root of 7 is about 2.6458. 7 is not a perfect square, so √7 is irrational: its decimals never end or repeat.
| Value | 2.64575131 |
|---|---|
| Rounded | 2.6 (1 dp) · 2.65 (2 dp) · 2.646 (3 dp) |
| Simplest radical form | √7 |
| Perfect square? | No — between 2² = 4 and 3² = 9 |
| 7 squared | 49 |
Estimating √7 in your head
Start from the nearest perfect square, 3² = 9. 7 is 2 less than that. Divide the difference by twice the root, 6, and subtract it:
√7 ≈ 3 − 2 ÷ 6 ≈ 2.667
The true value is 2.6458, so the one-step estimate is off by about 0.021. The estimate always comes out slightly high, and it is closest when 7 is near a perfect square. The method is explained in estimating square roots in your head.
Can √7 be simplified?
No. 7 has no perfect-square factor besides 1, so √7 is already in simplest radical form.
Frequently asked questions
What is the square root of 7?
The square root of 7 is about 2.6458. 7 is not a perfect square, so √7 is irrational: its decimals never end or repeat.
Is 7 a perfect square?
No. It lies between 2² = 4 and 3² = 9.
What is √7 in simplest radical form?
√7 is already in simplest form: 7 has no square factor other than 1.
Practise estimating square rootsNearby: √6 · √8 · all square roots to 150