The square root of 152 is approximately 12.33.
To understand how we arrive at this value, we can break it down. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, we are looking for a number that, when squared, equals 152.
The exact square root of 152 can be simplified as follows:
- 152 can be factored into 4 and 38 (since 4 x 38 = 152).
- The square root of 4 is 2, so we can rewrite the square root of 152 as: √152 = √(4 × 38) = √4 × √38 = 2√38.
To find a more precise decimal approximation, we can calculate the square root of 38.
When using a calculator, you will find that the square root of 38 is approximately 6.16. Therefore, if we multiply this by 2, we get:
2 × 6.16 ≈ 12.33.
This gives us the approximate value of the square root of 152, which is about 12.33.