How Do You Divide Radicals?


Quick Answer

A radical is a square root. To divide a radical or square root, put both radicals in a square root sign and divide them normally.

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Full Answer

Examples will provide the simplest way to show how to divide radicals. The first example is to divide the square root of 200 divided by the square root of 4. The first step is to combine the square roots under one radical, so the equation becomes the square root of 200/4. The second step is to make the necessary division. 200 divided by 4 is 50. The final step is to simply the radical, if possible.

The square root of 50 is the square root of 25 times the square root of 2. The square root of 25 is 5, so the final answer is the 5 times the square root of 2. The second example is the square root of 48 divided by the square root of 14. Put them both under the radical to make it the equation the square root of 48/14. Because these two numbers don't divide into each other, changing the radicals to different forms will simplify the equation. Radical 48 can be simplified into 4 times radical 3, which goes on top. The bottom cannot be simplified. The final equation ends up being 4 times radical 14/3.

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