How do you add and subtract radicals?


Quick Answer

Radicals can only be added or subtracted when they are the same or can be made the same through simplification. A radical can be simplified by factoring out the radical of a whole number and finding its square root.

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Full Answer

For example, two times the radical of three can be added to five times the radical of three for a total of seven times the radical of three. Addition and subtraction are possible in this instance because both numbers contain the radical of three. Adding together a radical of three with a radical of 75 is not possible until the radical of 75 is simplified.

To simplify, factor out the radical into 25 times three. Split the radical and write it as the radical of 25 times the radical of three. Then, find the square root of 25, which is five, and write the new radical as five times the radical of three. After simplifying the radical of 75 down to 5 times the radical of three, it is possible to add or subtract other radicals of three. For example, 10 times the radical of 3 plus the radical of 75 can be calculated as 15 times the radical of three.

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