Square root of 47
√47 ≈ 6.8557. The square root of 47 is about 6.8557. 47 is not a perfect square, so √47 is irrational: its decimals never end or repeat.
| Value | 6.8556546 |
|---|---|
| Rounded | 6.9 (1 dp) · 6.86 (2 dp) · 6.856 (3 dp) |
| Simplest radical form | √47 |
| Perfect square? | No — between 6² = 36 and 7² = 49 |
| 47 squared | 2,209 |
Estimating √47 in your head
Start from the nearest perfect square, 7² = 49. 47 is 2 less than that. Divide the difference by twice the root, 14, and subtract it:
√47 ≈ 7 − 2 ÷ 14 ≈ 6.857
The true value is 6.8557, so the one-step estimate is off by about 0.001. The estimate always comes out slightly high, and it is closest when 47 is near a perfect square. The method is explained in estimating square roots in your head.
Can √47 be simplified?
No. 47 has no perfect-square factor besides 1, so √47 is already in simplest radical form.
Frequently asked questions
What is the square root of 47?
The square root of 47 is about 6.8557. 47 is not a perfect square, so √47 is irrational: its decimals never end or repeat.
Is 47 a perfect square?
No. It lies between 6² = 36 and 7² = 49.
What is √47 in simplest radical form?
√47 is already in simplest form: 47 has no square factor other than 1.
Practise estimating square rootsNearby: √46 · √48 · all square roots to 150