Square root of 50
√50 ≈ 7.0711. The square root of 50 is about 7.0711, which simplifies to 5√2. 50 is not a perfect square, so √50 is irrational: its decimals never end or repeat.
| Value | 7.07106781 |
|---|---|
| Rounded | 7.1 (1 dp) · 7.07 (2 dp) · 7.071 (3 dp) |
| Simplest radical form | 5√2 |
| Perfect square? | No — between 7² = 49 and 8² = 64 |
| 50 squared | 2,500 |
Estimating √50 in your head
Start from the nearest perfect square, 7² = 49. 50 is 1 more than that. Divide the difference by twice the root, 14, and add it:
√50 ≈ 7 + 1 ÷ 14 ≈ 7.071
The true value is 7.0711, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 50 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √50
Find the largest perfect square that divides 50: it is 25, since 50 = 25 × 2. Take its root outside: √50 = √25 × √2 = 5√2.
Frequently asked questions
What is the square root of 50?
The square root of 50 is about 7.0711, which simplifies to 5√2. 50 is not a perfect square, so √50 is irrational: its decimals never end or repeat.
Is 50 a perfect square?
No. It lies between 7² = 49 and 8² = 64.
What is √50 in simplest radical form?
√50 = √(25 × 2) = 5√2.
Practise estimating square rootsNearby: √49 · √51 · all square roots to 150