when expressing 2 square root of 3 into a positive integer i seem to have the same answer as 3 square root of 2
how do you get the answer square root 12? and not square root 18?
sorry if i don't make any sense
Answers (2)
hello Helloyellowmia
It's good practice to make use of a certain Notation in order to convey meaning in a readable and unambiguous way:
n*m = the asterisk * is used for multiplication n times m, when necessary
n / m = division of n by m (n over m)
n^m = n to the m-th power
sqrt (n) = n^(1/2) = square root of n
And above all: Use of parentheses! Example: x + 2 / y - 6 looks nice and unambiguous written on a 2-dimensional piece of paper with x + 2 as the numerator, beneath that a neatly drawn fraction line, which works well as a delimiter, and beneath that y - 6 as the denominator.
BUT in a 1-dimensional representation, as in our line editor here, the expression
x + 2 / y - 6 equals x - 6 + 2/y.
We would have to use parentheses as delimiters for numerator and nominator:
(x + 2) / (y - 6) to make clear, what we want to say.
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I think, your question boils down to:
How is it that
2 times the square root of 3 equals the square root of 12
and
3 times the square root of 2 equals the square root of 18?
As 2 is the root of 2 squared:
2*2 = 2^2 = 4, and 2 = sqrt (4),
and 3 is the root of 3 squared:
3*3 = 3^2 = 9, and 3 = sqrt (9),
you can rewrite
2 * sqrt (3) = sqrt (12)
sqrt (2^2) * sqrt (3) = sqrt (12)
sqrt (4 * 3) = sqrt (12).
Same holds for
3 * sqrt (2) = sqrt (18)
sqrt (3^2) * sqrt (2) = sqrt (18)
sqrt (9) * sqrt (2) = sqrt (9 * 2) = sqrt (18).
I hope that helped.