Square root of 87
√87 ≈ 9.3274. The square root of 87 is about 9.3274. 87 is not a perfect square, so √87 is irrational: its decimals never end or repeat.
| Value | 9.32737905 |
|---|---|
| Rounded | 9.3 (1 dp) · 9.33 (2 dp) · 9.327 (3 dp) |
| Simplest radical form | √87 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 87 squared | 7,569 |
Estimating √87 in your head
Start from the nearest perfect square, 9² = 81. 87 is 6 more than that. Divide the difference by twice the root, 18, and add it:
√87 ≈ 9 + 6 ÷ 18 ≈ 9.333
The true value is 9.3274, so the one-step estimate is off by about 0.006. The estimate always comes out slightly high, and it is closest when 87 is near a perfect square. The method is explained in estimating square roots in your head.
Can √87 be simplified?
No. 87 has no perfect-square factor besides 1, so √87 is already in simplest radical form.
Frequently asked questions
What is the square root of 87?
The square root of 87 is about 9.3274. 87 is not a perfect square, so √87 is irrational: its decimals never end or repeat.
Is 87 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √87 in simplest radical form?
√87 is already in simplest form: 87 has no square factor other than 1.
Practise estimating square rootsNearby: √86 · √88 · all square roots to 150