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A square root is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 times 3 equals 9. In mathematical symbols, this is written as \( \sqrt{9} = 3 \). For any positive number \( x \), \( \sqrt{x} \) is a number that satisfies \( y^2 = x \). You will often see square roots when simplifying expressions or solving equations. Make sure to remember some basic square roots, like \( \sqrt{4} = 2 \) and \( \sqrt{16} = 4 \), as these frequently pop up in problems. Applying square roots to both numerator and denominator independently often helps to simplify complex fractions that include radicals.

In the given example, we separate the fraction under the square root as follows: \[ \frac{k}{100} = \frac{k}{10^2} \]. This allows us to apply the square root to both the numerator and the denominator individually, making the problem easier to handle.

Fraction simplification involves reducing a fraction to its simplest form, where the numerator and the denominator have no common factors other than one. This makes the fraction easier to work with. In the context of our problem, once we express the denominator as \( 10^2 \), we proceed to take the square root of both the numerator and the denominator: \[ \frac{\sqrt{k}}{\sqrt{10^2}} \].

Recall that \( \sqrt{a^2} = a \), meaning \( \sqrt{10^2} \) simplifies directly to 10. Thus, our expression simplifies to \[ \frac{\sqrt{k}}{10} \].

Always check if the fraction can be reduced further. In our case, the fraction is already in its simplest form once we apply the square root property.

Radical notation is used to represent roots of numbers. The most common radical is the square root, denoted by the symbol \( \sqrt{} \). For example, \( \sqrt{25} = 5 \) because 5 times 5 equals 25. Radicals can also be applied to variables and other expressions inside them. When simplifying expressions with radicals, it's important to know the properties, such as \[ \sqrt{a\cdot b} = \sqrt{a} \cdot \sqrt{b} \] and \[\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \].

In our case, the radical expression \[ \sqrt{\frac{k}{100}} \] simplifies by using these properties. This allows us to break it into two separate roots as \[ \frac{\sqrt{k}}{\sqrt{100}} \] which further simplifies into \[ \frac{\sqrt{k}}{10} \]. Understanding how to manipulate and simplify radicals is key to mastering more complex algebraic expressions