Square root of 75
√75 ≈ 8.6603. The square root of 75 is about 8.6603, which simplifies to 5√3. 75 is not a perfect square, so √75 is irrational: its decimals never end or repeat.
| Value | 8.66025404 |
|---|---|
| Rounded | 8.7 (1 dp) · 8.66 (2 dp) · 8.660 (3 dp) |
| Simplest radical form | 5√3 |
| Perfect square? | No — between 8² = 64 and 9² = 81 |
| 75 squared | 5,625 |
Estimating √75 in your head
Start from the nearest perfect square, 9² = 81. 75 is 6 less than that. Divide the difference by twice the root, 18, and subtract it:
√75 ≈ 9 − 6 ÷ 18 ≈ 8.667
The true value is 8.6603, so the one-step estimate is off by about 0.006. The estimate always comes out slightly high, and it is closest when 75 is near a perfect square. The method is explained in estimating square roots in your head.
Simplifying √75
Find the largest perfect square that divides 75: it is 25, since 75 = 25 × 3. Take its root outside: √75 = √25 × √3 = 5√3.
Frequently asked questions
What is the square root of 75?
The square root of 75 is about 8.6603, which simplifies to 5√3. 75 is not a perfect square, so √75 is irrational: its decimals never end or repeat.
Is 75 a perfect square?
No. It lies between 8² = 64 and 9² = 81.
What is √75 in simplest radical form?
√75 = √(25 × 3) = 5√3.
Practise estimating square rootsNearby: √74 · √76 · all square roots to 150