Square root of 145
√145 ≈ 12.0416. The square root of 145 is about 12.0416. 145 is not a perfect square, so √145 is irrational: its decimals never end or repeat.
| Value | 12.04159458 |
|---|---|
| Rounded | 12.0 (1 dp) · 12.04 (2 dp) · 12.042 (3 dp) |
| Simplest radical form | √145 |
| Perfect square? | No — between 12² = 144 and 13² = 169 |
| 145 squared | 21,025 |
Estimating √145 in your head
Start from the nearest perfect square, 12² = 144. 145 is 1 more than that. Divide the difference by twice the root, 24, and add it:
√145 ≈ 12 + 1 ÷ 24 ≈ 12.042
The true value is 12.0416, so the one-step estimate is off by less than 0.001. The estimate always comes out slightly high, and it is closest when 145 is near a perfect square. The method is explained in estimating square roots in your head.
Can √145 be simplified?
No. 145 has no perfect-square factor besides 1, so √145 is already in simplest radical form.
Frequently asked questions
What is the square root of 145?
The square root of 145 is about 12.0416. 145 is not a perfect square, so √145 is irrational: its decimals never end or repeat.
Is 145 a perfect square?
No. It lies between 12² = 144 and 13² = 169.
What is √145 in simplest radical form?
√145 is already in simplest form: 145 has no square factor other than 1.
Practise estimating square rootsNearby: √144 · √146 · all square roots to 150