Square root of 45
√45 ≈ 6.7082. The square root of 45 is about 6.7082, which simplifies to 3√5. 45 is not a perfect square, so √45 is irrational: its decimals never end or repeat.
| Value | 6.70820393 |
|---|---|
| Rounded | 6.7 (1 dp) · 6.71 (2 dp) · 6.708 (3 dp) |
| Simplest radical form | 3√5 |
| Perfect square? | No — between 6² = 36 and 7² = 49 |
| 45 squared | 2,025 |
Estimating √45 in your head
Start from the nearest perfect square, 7² = 49. 45 is 4 less than that. Divide the difference by twice the root, 14, and subtract it:
√45 ≈ 7 − 4 ÷ 14 ≈ 6.714
The true value is 6.7082, so the one-step estimate is off by about 0.006. The estimate always comes out slightly high, and it is closest when 45 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √45
Find the largest perfect square that divides 45: it is 9, since 45 = 9 × 5. Take its root outside: √45 = √9 × √5 = 3√5.
Frequently asked questions
What is the square root of 45?
The square root of 45 is about 6.7082, which simplifies to 3√5. 45 is not a perfect square, so √45 is irrational: its decimals never end or repeat.
Is 45 a perfect square?
No. It lies between 6² = 36 and 7² = 49.
What is √45 in simplest radical form?
√45 = √(9 × 5) = 3√5.
Practise estimating square rootsNearby: √44 · √46 · all square roots to 150