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 4^1/2 (4 raised to the power of ½ ) and see what happens when this is squared:

To square 4^1/2, 4^1/2 must be multiplied by itself giving:

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

This shows that when you multiply 4^1/2 by itself (squaring 4^1/2 ), the result is 4. In other words, 4^1/2 is another way of writing the square root of 4. This is defined as the positive square root and may be expressed as:

To satisfy yourself that this is correct, try using your calculator to work out 4^1/2.

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