Square root of 46
√46 ≈ 6.7823. The square root of 46 is about 6.7823. 46 is not a perfect square, so √46 is irrational: its decimals never end or repeat.
| Value | 6.78232998 |
|---|---|
| Rounded | 6.8 (1 dp) · 6.78 (2 dp) · 6.782 (3 dp) |
| Simplest radical form | √46 |
| Perfect square? | No — between 6² = 36 and 7² = 49 |
| 46 squared | 2,116 |
Estimating √46 in your head
Start from the nearest perfect square, 7² = 49. 46 is 3 less than that. Divide the difference by twice the root, 14, and subtract it:
√46 ≈ 7 − 3 ÷ 14 ≈ 6.786
The true value is 6.7823, so the one-step estimate is off by about 0.003. The estimate always comes out slightly high, and it is closest when 46 is near a perfect square. The method is explained in estimating square roots in your head.
Can √46 be simplified?
No. 46 has no perfect-square factor besides 1, so √46 is already in simplest radical form.
Frequently asked questions
What is the square root of 46?
The square root of 46 is about 6.7823. 46 is not a perfect square, so √46 is irrational: its decimals never end or repeat.
Is 46 a perfect square?
No. It lies between 6² = 36 and 7² = 49.
What is √46 in simplest radical form?
√46 is already in simplest form: 46 has no square factor other than 1.
Practise estimating square rootsNearby: √45 · √47 · all square roots to 150