Question 62071: I'm having a hard enough time in Algebra - now they want me to deal with "imaginary" numbers? I'm having trouble with simplifying (using i):
sqrt(-8) + sqrt(-50)
can someone help, please?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! I'll Try.
You know that the sqrt of a number is another number that, when multiplied by itself, yields the original number. For example, the sqrt of 9 is plus 3 or minus 3 since minus times minus equals a plus. Now, lets look at the sqrt
of -9. Clearly, there are no real numbers that can be multiplied by themselves to yield a -9. Thus, the definition "sqrt(-1)=i" and i is defined as an imaginary number.
Now we also know that the sqrt (-8) is equal to the sqrt (-1) times sqrt(8) which also equals sqrt(-1) times sqrt (4) times sqrt(2). simplifying:
sqrt (-1)=i
sqrt (4)=2
sqrt2=sqrt2
we now have:
sqrt(-8)=(2i)(sqrt (2))
Likewise sqrt (-50) equals sqrt (-1) times sqrt (50) which also equals sqrt (-1) times sqrt (2) times sqrt (25). simplifying, we have
sqrt (-1)=i
sqrt (25)=5
sqrt (2)=sqrt (2)
We now have:
sqrt(-50)=(5i)(sqrt(2)) Finally:
sqrt(-8)+sqrt(-50)= (2i)(sqrt(2))+(5i)(sqrt(2)) which equals
(sqrt(2))(5i+2i)=(7i)(sqrt(2))
Hope this helps. I know it does get confusing sometimes ----ptaylor
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