a-virginian

Recently in math I learned about simplifying radicals and radical operations.

First I reviewed the names of the parts of a radical.

Simplifying Radicals

Simplifying Perfect Square Roots

Lets take the equation $4\sqrt{50}$ . First you have to find the largest perfect square that can be multiplied to get the radicand. In this situation, the radicand is 50 so you can go through the cube roots table below until you find it.

Table of Perfect Cubes

square root	perfect square
1	1
2	4
3	9
4	16
5	25
6	36
7	49
8	64

In this situation, the largest perfect square would be 25. Next, you would seperate the radical into two. The eqaution would now look like this: $4\sqrt{25}\sqrt{2}$ . Next, simplify the the perfect square and multiply it with the number not squared. The equation is now solved and would look like this:

\[20\sqrt{2}\]

Perfect Cubes and Other Radicals

Simplifying other racidals is just like simplifying sqaure roots. First, you divide the radicand by a number to the power of the index. For example, if we have a cube root you use cubes. Also, if the index is a odd number, the root can be a negative number. If it is even, it can’t be negative. If there are variables, you can divde the variable by the index.

Multiplying, Adding and Subtracting

To multiply, add or subtract radicals, the radicands must be the same. If they are different, you could try to simplify them in a effort to make the radicands the same.

Dividing

First, check if the index is the same. If so, start by simplifying the coefficent, then the radicands, then you need to multiply both the denominator and the numerator by the bottom radicand. Finally, you simplify.