What is the sq root of -12 (imaginary number) and what is the sq root of -2
Thanks in advance
2007-01-11 13:19:03 · 6 answers · asked by mazp66 3 in Science & Mathematics ➔ Mathematics
√-1 = i
√-12 = √-1 times √12 = i times √4 times √3 = 2i√3
√-2=√-1 tiimes √2 = i√2
2007-01-11 13:23:50 · answer #1 · answered by crane 1 · 0⤊ 0⤋
√(-12) = 2(√3)i ~ 3.464i
√(-2) = (√2)i ~ 1.414i
Edit: If p is a positive real number, then the principal square root of (-p) is denoted by √(-p) and is defined to be the complex number (√p)i. The definition is motivated by the fact that (√pi)^2 = -p.
2007-01-11 13:24:30 · answer #2 · answered by S. B. 6 · 0⤊ 0⤋
Just put an i in front of the square root symbol and take away the negative. i is the imaginary number
2007-01-11 13:22:29 · answer #3 · answered by teh_general 2 · 0⤊ 0⤋
How did you be conscious the quadratic formulation? with the intention to finish that, your quadratic equation should be interior the type ax^2 + bx + c = 0. immediately, your quadratic equation is in vertex type. you want to first amplify the sq., so that you've (y+12)^2 - four hundred = (y^2 + 24y + one hundred forty four) - four hundred = y^2 + 24y - 256 = 0 And now it truly is in known type and also you may use the quadratic equation. notwithstanding, you are able to sparkling up this equation even extra common! achieve this by technique of the following: (y+12)^2 - four hundred = 0 (y+12)^2 = four hundred (y+12) = ±20 y = -12 ± 20 And both solutions are both genuine. they are 8 and -32. notwithstanding, the second one element of your question is a thanks to administration imaginary numbers. in case you truly had a sqrt(-2176), you should want to apply this rule: sqrt(ab) = sqrt(a) * sqrt(b) you are able to discover it really is genuine in case you undergo in ideas that a^x * b^x = (ab)^x if we modify a million/2 for x. accordingly, you are able to take sqrt(-2176) = sqrt(-a million) * sqrt(2176) = sqrt(2176) * i once you simplify sqrt(2176), you may have your answer. It seems to be 8i*sqrt(34) All you should do is save the i interior your answer, type of like yet another quantity. comparable to a thanks to assert (4*8) is the answer truly of 32, you are able to say 4i is the answer the position 4i can in simple terms be seen the multiplication of two numbers.
2016-11-23 13:04:32 · answer #4 · answered by schook 4 · 0⤊ 0⤋
square root of -12 = square root of 3 times square root of -4
square root of -4 is 2i
answer is 2i sqaure root of 3
:)
2007-01-11 13:28:52 · answer #5 · answered by Trevor Smith 3 · 0⤊ 0⤋
2sqr(3)i and -2sqr(3)i
2007-01-11 13:22:08 · answer #6 · answered by 7 · 1⤊ 0⤋