What is the square root of 60 to the nearest integer
The correct answer and explanation is:
Correct Answer: 8
The square root of 60 to the nearest integer is 8. To understand why, it helps to break down the concept of square roots and how to approximate them.
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 which, when squared, equals 60. Since perfect squares around 60 are 49 and 64, and their square roots are 7 and 8 respectively, the square root of 60 must lie between 7 and 8.
To get more precise, 7 squared is 49, and 8 squared is 64. Since 60 is closer to 64 than to 49, the square root of 60 must be closer to 8 than to 7. Using a calculator, the actual square root of 60 is approximately 7.745966692. When rounded to the nearest whole number, this becomes 8.
Understanding how to estimate square roots is useful in both mathematics and real-world applications. If the exact value is not needed, rounding to the nearest integer often gives a sufficiently accurate result. This is especially helpful in engineering, construction, and budgeting where approximations can simplify complex calculations.
It is also helpful to understand the properties of square roots. For example, square roots of numbers that are not perfect squares result in irrational numbers. These numbers cannot be expressed as exact fractions and have non-repeating decimal patterns. The square root of 60 is one such example. It cannot be simplified into a rational number, but it can be approximated for practical use.
In summary, because the actual value of the square root of 60 is about 7.75, the nearest whole number is 8.