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Square Roots Study Guide (page 2)

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Updated on Oct 3, 2011

Simplifying Radicals

Not all radicands are perfect squares. There is no whole number that, when multiplied by itself, equals 5. With a calculator, you can get a decimal that squares very close to 5, but it won't come out exactly. The only precise way to represent the square root of five is to write √5. It cannot be simplified any further.

There are three rules for knowing when a radical cannot be simplified any further:

  1. The radicand contains no factor, other than 1, that is a perfect square.
  2. The radicand cannot be a fraction.
  3. The radical cannot be in the denominator of a fraction.

Adding and Subtracting

Square roots are easy to add or subtract. You can add or subtract radicals if the radicands are the same. To add or subtract radicals, add the number in front of the radicals and leave the radicand the same. When you add 15√2 and 5√2, you add the 15 and the 5, but the radicand √2 stays the same. The answer is 20√2.

Multiplying and Dividing Radicals

To multiply radicals like 4√3 and 2√2, multiply the numbers in front of the radicals: 4 times 2. Then, multiply the radicands: 3 times 2. The answer is 8√6

    Try the following:
    5√3 · 2√2

Multiply the numbers in front of the radicals. Then, multiply the radicands. You will end up with 10√6.

To divide the radical 4√6 by 2√3, divide the numbers in front of the radicals. Then, divide the radicands. The answer is 2√2.

As opposed to adding or subtracting, the radicands do not have to be the same when you multiply or divide radicals.

Find practice problems and solutions for these concepts at Square Roots Practice Questions.

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