Square root of 42
√42 ≈ 6.4807. The square root of 42 is about 6.4807. 42 is not a perfect square, so √42 is irrational: its decimals never end or repeat.
| Value | 6.4807407 |
|---|---|
| Rounded | 6.5 (1 dp) · 6.48 (2 dp) · 6.481 (3 dp) |
| Simplest radical form | √42 |
| Perfect square? | No — between 6² = 36 and 7² = 49 |
| 42 squared | 1,764 |
Estimating √42 in your head
Start from the nearest perfect square, 6² = 36. 42 is 6 more than that. Divide the difference by twice the root, 12, and add it:
√42 ≈ 6 + 6 ÷ 12 ≈ 6.5
The true value is 6.4807, so the one-step estimate is off by about 0.019. The estimate always comes out slightly high, and it is closest when 42 is near a perfect square. The method is explained in estimating square roots in your head.
Can √42 be simplified?
No. 42 has no perfect-square factor besides 1, so √42 is already in simplest radical form.
Frequently asked questions
What is the square root of 42?
The square root of 42 is about 6.4807. 42 is not a perfect square, so √42 is irrational: its decimals never end or repeat.
Is 42 a perfect square?
No. It lies between 6² = 36 and 7² = 49.
What is √42 in simplest radical form?
√42 is already in simplest form: 42 has no square factor other than 1.
Practise estimating square rootsNearby: √41 · √43 · all square roots to 150