Posted by shansen1@pacbell.net (66.126.108.56) on October 01, 2003 at 01:25:20:
In Reply to: SIMPLIFY RADICALS posted by on September 30, 2003 at 18:35:23:
Try to use the ASCII notation convention for square roots (exponents) which is the caret ^ symbol. Your notation V2 means SQRT 2. SQRT 2 means "2 to the one half power" which is equal to 1.4142 and written in ASCII as 2^1/2.
Theorem you will need to understand and work this problem. Law of exponents (a^b)^c = a^(b*c)
a,b,c can be any real numbers.
Problem 1 restated with ASCII convention:
2^1/2 + (2/49)^1/2
Notice that 49 is a perfect square. 49 = 7*7. The square root of 49 is 7. Therefore:
2^1/2 + (2/49)^1/2 = 2^1/2 +(2/7^2)^1/2
Since (7^2)^1/2 = 7 according to the law of exponents above, the expression simplifies to
2^1/2 +(2^1/2)/7 = (6/7)2^1/2 = 1.21218
Done
Problem 2
3*2^1/2 + 50^1/2
Note that 50 = 25*2 and that 25 is a perfect square.
25 = 5*5 Therefore:
3*2^1/2 + 50^1/2 = 3*2^1/2 + (5^2*2)^1/2
Since (5^2)^1/2 = 5 by the law of exponents above, the expression becomes
3*2^1/2 + 5*2^1/2 = 8*2^1/2 = 11.3137
Done
PS: Until you are 'solid' with these problems, use a calculator to check your work. This will help you to uncover and understand your mistakes as well as reinforce your learning. Good luck!