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quacker
ANSWERS: 4
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"root two i" where "root two" is the number whose square is 2. So approximately, the answer is 1.41 i. This is the principal square root. There is another one: "minus root two i" Once i is invented, no more letters are needed to solve equations containing roots as all such so called complex numbers can be written in the form a + b i, where a and b are real numbers.
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Square root of the product of two numbers a and b is equal to the product of the square roots of the numbers provided atleast one of the numbers is a positive real number. Since -2 can be written as the product of 2 and -1 where 2 is a positive real number, the square root of -2 is the square root of 2 multiplied by the square root of -1. Hence the square root of -2 is twice the value of i. In reply to comment 1:I'm sorry.My last sentence is wrong.The answer is "square root of -2 is the product of square root of two and i" .
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You cannot have a square root on a minus number no number that is squared can ever make a minus number because: a minus x a minus makes a plus (e.g. -1 * -2 = +2) a plus x a minus makes a minus BUT then the numbers arn't the same (e.g. -1 * 2 = -2) a plus x a plus makes a plus (e.g. +1 * +2 = +2) try it on a calculator, if you do a sqare root of a negative number, it will come up with error.
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Remember that: sqrt(x*y) = sqrt(x)*sqrt(y) So: sqrt(-2) = sqrt(-1)*sqrt(2) = i*sqrt(2) or, approximately 1.41*i.
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