What is the square root of -1?
89444
The answer is "i" because there is no number, that when mutliplied by itself, will give you -1.  Think about it: the only possible combination that would make sense is 1 X 1, which equals 1...not -1.
926410
the fallacy is square root of (-1)^2=-1 and not mod -1
981873
-7 and -sqrt49\n\nYou can not take a square root of a negative number. Well, you can, but it's called an imaginary number because it can't actually exist.
87424
For negative exponents, make a fraction of 1 over whatever the base number is.  Then raise the denominator to the positive of your exponent.\n\nIn this case 10^(-2) would be 1/10^2 (read "1 over ten squared) so the answer is 1/100\n\nSome other examples:\n\n2^-5 = 1/(2^5)\n\n4^(-1/2) = 1/(4^1/2) or 1/sqrt4
319669
did you mean the square root of x-1 = 3?\nin that case it will be 2:\nadd positive 1 to both sides:\n   x-1+1= 3+1\nthen solve the remaining equation:\n   x=4\nget the square root of 4:\n   x=2
441224
x - sqrt(x) = 0\nAdd sqrt(x) to each side\nx = sqrt(x)\nSquare each side\nx^2 = x \nSubtract x from each side\nx^2 - x = 0\nFactor x\nx(x-1) = 0\nx = 0 or x = 1\nCheck in orginal problem: x- sqrt(x) = 0\nFor x = 0\n0 - sqrt(0) = 0\n0 - 0 = 0 \n0 = 0\nFor x = 1\n1 - sqrt(1) = 0\n1 - 1 = 0\n0 = 0\nThus, the answers are \n0 and 1\n\nAlso, sqrt(x^2) = x is only tru if x is positive.\nsqrt(x^2) = |x| is true for any number.\nThat is, the square root of x^2 is equal to the absolute value of x.\n\nx^2 = 4 means x = -2 or x = 2
105888
square root(pi) = 1.77245385
307994
The square root of negative 1 is the number, which multiplied by itself, gives negative 1.  Any real positive number when multiplied by itself gives a positive number.  Any real negative number when multiplied by itself gives a positive number.  Therefore no real number can be the square root of negative 1.\n\nHowever, it is useful to create a system of mathematics where negative one has a square root.  To do this we think of all the real numbers as belonging to a line.  We create another line, perpendicular to this line, and intersecting at zero.  We call this line the imaginary axis.  Then we invent rules for multiplying points in the plane defined by the real axis and the imaginary axis.  The way mathematicians have defined these things, the unit 1 on the positive imaginary axis when multiplied by itself is equal to negative 1.
915401
this means\n\nx^3 = -1\nor x^3+1 = 0\n\nf(x) = x^3+1\n\nf(-1) = 0\nso one root is -1\n\nfor the other root by division\n(x+1)(x^2-x+1)\nx^2-x+1 = 0 => x= (1+/-sqrt(3)i)/2
50988
The square root of 144 is 12 and -12. The principal square root is 12.
907350
1) sqrt(x - 1) = x - 3\nSquare both sides:\nx - 1 = (x - 3)²\nx - 1 = x² -6x + 9\nx² -7x + 10 = 0\n(x - 2)(x - 5) = 0\nx = 2 or x = 5\n\nAs a double-check:\nsqrt(2 - 1) = 2 - 3\nsqrt(1) = -1 <-- this is a true statement since 1 and -1 are roots.\n\nsqrt(5 - 1) = 5 - 3\nsqrt(4) = 2 <-- check\n\n2) sqrt(y + 12) = 2\nSquare both sides:\ny + 12 = 2²\ny + 12 = 4\ny = -8\n\nAs a double-check:\nsqrt(-8 + 12) = 2\nsqrt(4) = 2 <-- correct\n\nSo your answers are:\n1) x = 2 or x = 5\n2) y = -8
284143
j * sqrt(pi)\n\nj = i; which is imaginary number which is sqrt(-1)\nsqrt is "square root"
491468
If by x1/2 you mean x^(1/2), and by -1-[x] you mean -1 minus the absolute value of x, then the composite function f o g is (-1-[x])^(1/2).\n\nWhat is unusual about this is that this function is not defined for any real number x.  The expression (-1-[x]) is always going to be negative, no matter what x is.  Raising this to the power of 1/2 is the same as taking the square root of it.  Since the square root of a negative number is not defined in the real number system, the domain is the empty set.
270378
-12 and 10 are both correct since\n\n-12 + 1 = -11 and | -11 | is 11\n\n10 + 1 = 11 and | 11 | is 11
670743
There is no square root of -1.
948937
(-3,-3);(-2,0);(-1,1);\n(0,0);(1,-3)
218797
sqrt(157452304)= +/-12548\n\ndon't forget that 2 negatives cancel out so every number has 2 square roots (either rational or irrational) , one positive and one negative.