Express in simplest radical form.
square root of 100
The Correct Answer and Explanation is :
To express the square root of 100 in simplest radical form, we start by simplifying the expression:
[
\sqrt{100}
]
The square root of a number is the value that, when multiplied by itself, gives the original number. In this case, we are looking for the number that, when squared, equals 100.
We know that:
[
10 \times 10 = 100
]
Thus:
[
\sqrt{100} = 10
]
So, the square root of 100 simplifies directly to 10. There is no need for further simplification because 10 is already in its simplest form.
Explanation of the process:
- Identifying Perfect Squares: A perfect square is a number that is the square of an integer. In this case, 100 is a perfect square because ( 10 \times 10 = 100 ). Since 100 is a perfect square, its square root is an integer, specifically 10.
- Simplifying Square Roots: To simplify square roots, we often factor the number under the radical. If the number can be broken down into smaller factors that are perfect squares, we can simplify the radical. For example, if we were simplifying ( \sqrt{200} ), we could factor 200 as ( 100 \times 2 ), and then take the square root of 100, which is 10. This would leave us with:
[
\sqrt{200} = \sqrt{100 \times 2} = \sqrt{100} \times \sqrt{2} = 10\sqrt{2}
]
However, in the case of ( \sqrt{100} ), since 100 is already a perfect square, we do not need to factor further.
Conclusion:
Thus, ( \sqrt{100} = 10 ) is already in its simplest radical form, as no further simplification is needed. The square root of any perfect square is simply the positive integer that, when multiplied by itself, gives the original number.