Question 388398
{{{root(7, 30)}}}
30 is not the 7th power of any number one can find manually. Nor does it have any 7th power factors (other than 1). So we cannot simplify this expression manually either.<br>
But most calculators can find a decimal approximation for this. All we really need is a button for exponentiation. The button looks like "^" on many calculators. On some calculators the exponentiation button looks like {{{x^y}}}.<br>
The reason an exponentiation button will help is that
{{{root(7, 30)}}}
is the same as
{{{30^(1/7)}}}
So all we have to do is get your calculator to raise 30 to the 1/7 power. If your calculator has parentheses buttons, too, then you can literally type:
30^(1/7)
If your calculator does not have buttons for parentheses, then you have to get a decimal for 1/7 first. 1/7 is approximately 0.142857143. So you would type
30^0.142857143<br>
P.S. In response to the question in your email...
1) You obviously have access to a computer. Look on the computer for a calculator program. Most computers have such a program. (If you use Windows you may find it in the Accessories folder.) The program may have the buttons you need to raise numbers to powers.<br>
2) Unless your calculator only cost less than about $5, I am truly amazed that your calculator has no way to raise numbers to powers. You may want to double check. Maybe it's a "shift" or "2nd" function key. If you have the manual/instructions for the calculator, look in there for exponents, powers or exponentiation.<br>
3) If your calculator has buttons for "log" and "log<sup>-1</sup>" then there is still a way:
3a) Use your calculator to find log(30)
3b) Divide the log(30) by 7
3c) Find log<sup<-1</sup> of the result from the previous step.
However, if your calculator really has no way to raise numbers to powers, it is unlikely to have buttons for "log" and "log<sup>-1</sup>"!?<br>
4) A table of logarithms can help. Your Math book may have one in the back. (They used to be popular before calculators with logarithm keys became so inexpensive.) If you find a table of logarithms...
4a) Look up the log of 3
4b) Add 1 to the log of 3
4c) Divide that result by 7
4d) Look up the number whose logarithm is the result from 4c.<br>
5) It looks like you are out of luck if none of the above help and you are unable to buy a calculator with these keys.