Square root of 53
√53 ≈ 7.2801. The square root of 53 is about 7.2801. 53 is not a perfect square, so √53 is irrational: its decimals never end or repeat.
| Value | 7.28010989 |
|---|---|
| Rounded | 7.3 (1 dp) · 7.28 (2 dp) · 7.280 (3 dp) |
| Simplest radical form | √53 |
| Perfect square? | No — between 7² = 49 and 8² = 64 |
| 53 squared | 2,809 |
Estimating √53 in your head
Start from the nearest perfect square, 7² = 49. 53 is 4 more than that. Divide the difference by twice the root, 14, and add it:
√53 ≈ 7 + 4 ÷ 14 ≈ 7.286
The true value is 7.2801, so the one-step estimate is off by about 0.006. The estimate always comes out slightly high, and it is closest when 53 is near a perfect square. The method is explained in estimating square roots in your head.
Can √53 be simplified?
No. 53 has no perfect-square factor besides 1, so √53 is already in simplest radical form.
Frequently asked questions
What is the square root of 53?
The square root of 53 is about 7.2801. 53 is not a perfect square, so √53 is irrational: its decimals never end or repeat.
Is 53 a perfect square?
No. It lies between 7² = 49 and 8² = 64.
What is √53 in simplest radical form?
√53 is already in simplest form: 53 has no square factor other than 1.
Practise estimating square rootsNearby: √52 · √54 · all square roots to 150