SOLUTION: Use a calculator to find the approximate decimal value of the follow rational and irrational numbers. Round to the nearest tenth. -2(to the square root of)5 and (cubed roo

Algebra ->  Square-cubic-other-roots -> SOLUTION: Use a calculator to find the approximate decimal value of the follow rational and irrational numbers. Round to the nearest tenth. -2(to the square root of)5 and (cubed roo      Log On


   

Question 101827: Use a calculator to find the approximate decimal value of the follow rational and irrational numbers. Round to the nearest tenth.
-2(to the square root of)5
and
(cubed root of)-15
[Sorry if that doesn't make sense but I don't know how to make a square root symbol]
I thought that these didn't have answers because you can't have negative square roots?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I think you're asking about the fifth root of (-2) and the cube root of (-15), that is, what number x would give me x%2Ax%2Ax%2Ax%2Ax=-2 and what number z would give me z%2Az%2Az=-15. You are correct that there are no real numbers that you can square to give you a negative number. In fact that's true for all of the even powers but the odd powers you can. For example, %28-1%29%2A%28-1%29%2A%28-1%29=-1, so the cube root of -1 is -1. To solve your problem, find the fifth root of 2 and place a negative sign in front of it. The same for the cube root of -15. Find the cube root of 15 and put a negative sign in front.
2%5E%281%2F5%29=1.14869 and 15%5E%281%2F3%29=+2.46621. You only need to the nearest tenth and don't forget the negative sign.
The fifth root of (-2) = -1.1 (rounded down)
The cube root of (-15) = -2.5 (rounded up)
Let's check our answer (-1.1)*(-1.1)*(-1.1)*(-1.1)*(-1.1)= -1.61. What happened? Since we only rounded to the tenths, our answer isn't that close. If we had rounded to the hundreths (1.15, rounded up), the answer would have been 2.011, definitely closer. Good luck.