Square root of 90
√90 ≈ 9.4868. The square root of 90 is about 9.4868, which simplifies to 3√10. 90 is not a perfect square, so √90 is irrational: its decimals never end or repeat.
| Value | 9.48683298 |
|---|---|
| Rounded | 9.5 (1 dp) · 9.49 (2 dp) · 9.487 (3 dp) |
| Simplest radical form | 3√10 |
| Perfect square? | No — between 9² = 81 and 10² = 100 |
| 90 squared | 8,100 |
Estimating √90 in your head
Start from the nearest perfect square, 9² = 81. 90 is 9 more than that. Divide the difference by twice the root, 18, and add it:
√90 ≈ 9 + 9 ÷ 18 ≈ 9.5
The true value is 9.4868, so the one-step estimate is off by about 0.013. The estimate always comes out slightly high, and it is closest when 90 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √90
Find the largest perfect square that divides 90: it is 9, since 90 = 9 × 10. Take its root outside: √90 = √9 × √10 = 3√10.
Frequently asked questions
What is the square root of 90?
The square root of 90 is about 9.4868, which simplifies to 3√10. 90 is not a perfect square, so √90 is irrational: its decimals never end or repeat.
Is 90 a perfect square?
No. It lies between 9² = 81 and 10² = 100.
What is √90 in simplest radical form?
√90 = √(9 × 10) = 3√10.
Practise estimating square rootsNearby: √89 · √91 · all square roots to 150