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Succeed with maths: part 2
Succeed with maths: part 2

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3.1 Square roots in power notation

Using power notation to show a root is very useful for further maths, when you may need to show roots using this method to help solve a problem. By using the rules for multiplication of powers from 2.1 Multiplying powers with the same base number this week it is possible to work out the appropriate value of the power. Remember that when multiplying powers with the same base, the power in the answer will the sum of the original powers.

So, let’s consider the following example of 41/2 (4 raised to the power of ½ ) and see what happens when this is squared:

To square 41/2, 41/2 must be multiplied by itself giving:

four super one solidus two multiplication four super one solidus two

To work out the answer to this, add the powers together:

equation sequence four super one solidus two multiplication four super one solidus two equals four super open one solidus two plus one solidus two close equals four super one equals four

This shows that when you multiply 41/2 by itself (squaring 41/2 ), the result is 4. In other words, 41/2 is another way of writing the square root of 4. This is defined as the positive square root and may be expressed as:

equation sequence four super one solidus two equals Square root of four equals two

To satisfy yourself that this is correct, try using your calculator to work out 41/2.

There is one final point to consider about square roots before finishing, and that is the square root of a negative number.