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How to Divide a Number by Square Roots

If you take a high school or college algebra or calculus course, you will have to perform calculations pertaining to square roots. A square root is a number that you multiply times itself to equal a specific value. For instance, the square root of 4 is 2, because 2 times 2 equals 4. The symbol for a square root is called a radical sign, and the number beneath this symbol is the radicand. If you must divide a number by a square root, there is a simple process that you must follow.

Instructions

    • 1

      Write down the problem. You might, for instance, have the following example: 5/√25.

    • 2

      Extract the square root from the denominator (bottom of the fraction) if the number is a perfect square. That means a whole number times itself equals the radicand. In this example, you would extract 5 because 5 times 5 equals 25.

    • 3

      Divide the numerator (top number) by the denominator. In this example, you would divide 5 by 5 to get 1 as your answer.

    • 4

      Multiply the numerator and denominator by the square root in the denominator if the number isn't a perfect square or if the radicand is a variable (a letter that represents a number). For example, if you have 2/√x, you would multiply the top and bottom of the fraction by √x. This would give you 2√x/x. A numerical example is as follows: 6/√5. Multiply the top and bottom by √5 to get 6√5/5. You can further simplify this by calculating the square root of 5 (2.236). Then you would multiply this value times 6 to get 14.416 and then divide by 5 to get 2.6832.

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