Square root of 73
√73 ≈ 8.544. The square root of 73 is about 8.544. 73 is not a perfect square, so √73 is irrational: its decimals never end or repeat.
| Value | 8.54400375 |
|---|---|
| Rounded | 8.5 (1 dp) · 8.54 (2 dp) · 8.544 (3 dp) |
| Simplest radical form | √73 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 73 squared | 5,329 |
Estimating √73 in your head
Start from the nearest perfect square, 9² = 81. 73 is 8 less than that. Divide the difference by twice the root, 18, and subtract it:
√73 ≈ 9 − 8 ÷ 18 ≈ 8.556
The true value is 8.544, so the one-step estimate is off by about 0.012. The estimate always comes out slightly high, and it is closest when 73 is near a perfect square. The method is explained in estimating square roots in your head.
Can √73 be simplified?
No. 73 has no perfect-square factor besides 1, so √73 is already in simplest radical form.
Frequently asked questions
What is the square root of 73?
The square root of 73 is about 8.544. 73 is not a perfect square, so √73 is irrational: its decimals never end or repeat.
Is 73 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √73 in simplest radical form?
√73 is already in simplest form: 73 has no square factor other than 1.
Practise estimating square rootsNearby: √72 · √74 · all square roots to 150