91Ó°ÊÓ

A radical expression involves roots, such as square roots, cube roots, etc. They can include numbers, variables, or both.
For the square root, the radical sign \( \sqrt{} \) is used. Inside the radical, the value is called the radicand.
For example, in \( \sqrt{x} \), \( x \) is the radicand.
It's important to remember that the square root of a positive number always has two values: a positive and a negative root, typically only the positive root is considered when we work with variables representing positive numbers.
When simplifying a radical expression, our goal is to express it in the simplest form. For instance, \( \sqrt{700 x} \) can sometimes be simplified, especially when we are dealing with quotients as in our example exercise.

The quotient property of radicals is a helpful tool for simplifying expressions involving radicals.
The property states that the square root of a quotient is the same as the quotient of the square roots.
Mathematically, it looks like this: \ \( \frac{ \text{sqrt}(a) }{ \text{sqrt}(b) } = \sqrt{ \frac{a}{b} } \)
This property allows us to combine the radicals and simplify the expression.
For instance, in the exercise \( \frac{ \sqrt{700 x} }{ \sqrt{7 x} } \), we apply the quotient property of radicals like this: \( \sqrt{ \frac { 700 x }{ 7 x } } \. \)
The variables \( x \) cancel out, making the expression simpler to handle.

Calculating the square root involves finding a number which, when multiplied by itself, gives the original number.
For simple square roots, you might already know some common values by heart, such as \( \sqrt{1}=1, \sqrt{4}=2, \sqrt{9}=3, \sqrt{16}=4, \sqrt{25}=5, \) and so forth.
In the context of our problem, after applying the quotient property of radicals and simplifying the expression \( \sqrt{ 100 } \), we find that the square root of 100 is 10.
This solution comes from the fact that \( 10 \text{×} 10 = 100 \).
So, our final answer for the original problem \( \frac{ \sqrt{700 x} }{ \sqrt{7 x} } \) is simply 10.