9.05+Powers+and+roots

Powers and roots!
 * Lucy and Cassy **

The power, index or exponant ( these all mean the same!) indicates how many times the base number is to be multipled by itself. eg 2^4= 2x2x2x2. So 2^4 = 16 2 is the base number, and 4 is the exponent. Roots are exsactly the opposite, in that you have to find the number that when multiplied by the exponanant gives you the base number. So the square root of 81 = 9 because 9x9 =81

__Finding square numbers __

In square numbers the exopnant is 2. So 10 squared is 10^2 or 100. So, if a question asks the square number of 10, you will just times 10 by itself. (10^2 or 10x10) To do this on a calculater you press the base number you want, then the butten tht looks like this ^ and then the exponant 2.

__Finding square roots __

To find the root of a number, you must find a number multiplied by itself to equal the base number. eg, the square root of 49 is 7, as 7x7=49. in a test, this may be represented as a tick with a line on the end with the base number inside. To find the square root on a calculater, you look for this symbol and then press the base number you want.

__Finding cube numbers __

In cube numbers the exponent is 3. So 5 cubed is then same as 5^3 or 125. So, if a question asks the cubed number of 5, you will just times 5 by itself 3 times. (5^3 or 5x5x5) To do this on a calculater you press the base number you want, then the butten tht looks like this ^ and then the exponant 3.

__Finding cube roots __ To find the cubed root of a number, you must find a number multiplied by itself three times to equal the base number. eg, the cube root of 125 is 3, as 3x3x3=125. in a test, this may be represented as a small three infront of a tick with a line on the end, with the base number inside. To find the cube root on a calculater, press shift then the butten x3 then press the base number you want.

__Calculating other powers e.g. 3^5 __ When calculating other powers, you calculate the same way as cubed or squared numbers, but with a different exponent. For example, when given the equation 3^5 it is worked out 3x3x3x3x3. So the answer is 243

__Finding terms in patterns involving square numbers __ An example of a pattern involving square numbers is.. 1, 4, 9, 16, 25, 36

<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 110%; margin-bottom: 0cm;">The pattern here is 1^1, 2^2, 3^3, 4^4, 5^5 and 6^6. <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 110%; margin-bottom: 0cm;">Another one is,

<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 110%; margin-bottom: 0cm;">1, 8, 27, 64, 125

<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; font-size: 110%; margin-bottom: 0cm;">What do you think is the patern here?

.media type="youtube" key="eR-ML0S__DI?fs=1" height="385" width="480" Here is a video to help with learning. You do not have to know about the exponents of a negative number, but it might be benifitial to watch the rest! :)