But my steps above show how you can switch back and forth between the different formats (multiplication inside one radical, versus multiplication of two radicals) to help in the simplification process.
In case you're wondering, products of radicals are customarily written as shown above, using "multiplication by juxtaposition", meaning "they're put right next to one another, which we're using to mean that they're multiplied against each other". You don't want your handwriting to cause the reader to think you mean something other than what you'd intended.
The Square root meaning of a number can be simply be defined as a number that has an equivalent value to two numbers multiplied by themselves.
The numbers are usually the same when multiplied with one another and the square root is the number taken from it.
Generally, the square root only takes the positive value of . Square roots can also be written in exponential notation, so that is equal to the square root of .
The square root (or the principle square root) of a number is denoted . When we consider only positive reals, the square root function is the inverse of the squaring function.Note that this agrees with all the laws of exponentiation, properly interpreted.For example, , which is exactly what we would have expected.To indicate some root other than a square root when writing, we use the same radical symbol as for the square root, but we insert a number into the front of the radical, writing the number small and tucking it into the "check mark" part of the radical symbol.This tucked-in number corresponds to the root that you're taking.Finding the square root of a number is the inverse operation of squaring that number.: No, As per the square root definition, negative numbers shouldn’t have a square root.Because if we multiply two negative numbers result will always be a positive number.When doing this, it can be helpful to use the fact that we can switch between the multiplication of roots and the root of a multiplication.In other words, we can use the fact that radicals can be manipulated similarly to powers: .To simplify this sort of radical, we need to factor the argument (that is, factor whatever is inside the radical symbol) and "take out" one copy of anything that is a square.That is, we find anything of which we've got a pair inside the radical, and we move one copy of it out front.