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When arranging radicals, it is important to consider the index of the radical, whether or not the radical is mixed or entire, and then the radicand.
There are three steps on how to evaluate a radical. Some of the step-by-step instructions are multiply two radicals with the same index number by simply multiplying the numbers beneath the radicals, divide a radical by another radical with the same index number by simply dividing the numbers inside, and simplify large radicals using the product and quotient rules of radicals.
When adding and subtracting radicals, you can only combine radicals with the same index and radicand (the number inside the radical). Here are some examples:
electronegative radicals are anions or acid radicals.
2 radicals are similar (like terms) if, when in simplified form, the index is the same, and the radicand is the same. The coefficient may be different. EX: 3(sq root 2) and 5(sq root 2) are like terms, but 3(cube root 2) is not a like term for either.