What is the square root of -4?
140009
Note that it has two answers:\n\na^2=-4 ---> a=2i or a=-2i\n\n(2i)^2=2^2*i^2=4*(-1)=4\n\nand\n\n(-2i)^2=(-2)^2*i^2=4*(-1)=4
140600
sqrt 4 is the same as 4^(1/2), so the question becomes 4^5/4^(1/2)\n\nWhen dividing, if the bases (in this case 4) are the same, then you can subtract the exponents.  5 - 1/2 = 4 1/2, or 9/2.  So now you have 4^(9/2).\n\nAlso, in a fractional exponent, the denominator is a root, and the numerator is the power it is raised to, so 4^(9/2) is like saying the 2nd root of 4, raised to the 9th power.  This is written as (sqrt 4)^9
1096915
Grab a caluclator.  Read what it says when you enter the square root of 4.  It gives you 2... 2 only, and not -2.\n\nA square root is a function, meaning it can only have one value.  A bunch of fellow math geeks a long time ago decided the non-negative one was better.\n\nIt's kind of like inverse trig functions.  The sine of a 0° angle is 0.  The sine of a 180° angle is 0.  So are the sines of 360°, 540°, -180°, and so on.  When it comes to the arcsine, though, arcsin(0) could equal -180°, 0°, 180°, 360°, or any of a host of others.  To make the Arcsin a function, the math geeks picked one, Arcsin(0) = 0°.\n\nYes, (2)(2) = 4.  Yes, (-2)(-2) = 4.  But 4 has only one square root, and it's 2.  People answering otherwise are thinking of solving the equation:\nx² = 4, which does have two solutions... x = 2 or -2.\n\nx² = 4\nSqRt(x²) = SqRt(4)  [Take the square root of both sides.]\n|x| = 2  [Simplifying.  Note on the right side, the square root of 4 is 2.  It's a function, and can only have one value.  On the left, taking a square root of a variable that would leave an odd power (x^1) means the expression must be an absolute value.]\nx = 2 or -2.  [It's solving the absolute value part of this problem that yields plus or minus 2.]\n\nAn equation [like x² = 4, or sin(a)=0] can have many solutions.\nA function [like the square root of 4, or Arcsin(0)] can have only one value.
712192
are you working out:\n\nsqrt(-8) x sqrt(-10) ?\n\nif so, this is a complex number.\n\nsqrt(-8) x sqrt(-10)\n= i x sqrt(8) x i x sqrt(10)\n= i^2 x sqrt(80)\n\nand we know that i^2 = -1, so:\n\n= -1 x 8.94\n= -8.94
152568
2i. The character "i" denotes the square root of -1, which is not a real number. So, the sq. root of -4 is 2i.
941657
Nah, sorry, but something in your thinking is incorrect.  You seem to be saying that if you add the square root of 3 four times, you want to get 9.  That's not right.  If you take sqrt(3)^4, you WILL get 9.   Taking the fourth root of a number is not like dividing a pie into four pieces.
980680
use the quadradic formula then:\n\ny^2 + y - 30 = 0\n\n(-1 +/- sqrt(1- 4 (-30)) )/ 2\n\ny=(-1 +/- 11 ) 2\n\n-6, 5 are your two answers. 10 points please ! :)
593847
The answer is zero isn't it?  The square root of (7 squared) is 7.  If you minus 14 you get -7. Add another 7, brings you up to zero.
169693
the absolute value of -4 (usually written |-4|) is 4\n\ntherefore (-2) - |-4| = (-2) - 4 = -6\n\n-6
909263
The square root of -1 cannot be a real number, because there's no number which, when multiplied by itself, gives -1.  So the square root of any negative number cannot be a real number, because for any number -n, it is equal to -1 x n.  You can take the square root of the positive n, but not the -1.  We call the square root of negative one by the letter "i", standing for "imaginary".  The square root of -16 would be +/-4i.  Zero is a real number, because it denotes the number of things when there aren't any, and it is a placeholder for the origin of a real line.  Negative numbers are also real numbers, as used on a number line, or as a measure of the balance in your bank account if you go into your line of credit.
283638
sqrt(25)=5 or -5. To verify it:\n\n5*5=25 checks\n-5*-5=25 checks\n\nboth work.\n\nan important thing to remember while square-rooting a number is that the root can be both positive or negative, as two negatives multiply up to a positive.
607013
Another Method.\n\n-1 = -1\n\n-1/1 = 1/-1\n\nSquare root both sides,\n\nSQR(-1/1) = SQR (1/-1)\n\nExpanding,\n\nSQR(-1)/SQR(1) = SQR(1)/SQR(-1)\n\nSQR(-1)/1 = 1/SQR(-1)\n\nCross Multiply,\n\nSQR(-1)*SQR(-1) = 1\n\n(SQR(-1))^2 = 1\n\n-1 = 1\n\nDivide by 2 on both sides,\n\n-1/2 = 1/2\n\nAdd 3/2 to both sides,\n\n-1/2 + 3/2 = 1/2 + 3/2\n\n1 = 2 (ans)
775585
-5+-sqr(25-4(2)(-9))/4\n-5+-sqr(97)/4\n1.21 and -3.71
966435
square root of 40.5 = 6.363961.\n\nAnd for the future.... http://www.calculator.com/
169153
= -4^2\n= -1 * (4^2)\n= -1 * 16\n= -16\n\nif you type in -4² on your calculator you get -16.\n\nBUT\ntwo negative numbers make a positive so it could be 16.  however, that is only if it says either\n\n(-4)² \nor\n-4*-4\n\nbut because your questions says -4², i would say -16.
171301
The square root of 3 is an irrational number, however, we can approximate it using a bit of calculus.\n\nWe know the sqrt of 4 = 2.  4 is pretty close to 3, so we can estimate the sqrt of 3 to be,\nsqrt(4) - (1/(2*sqrt(4)))*(1) = 1.75\n\nBy plugging sqrt(3) into a calculator, we get about 1.732060808, which is pretty close to our estimate.  The close the numebr you choose to 3, the closer your estimate will be to the "true" value.
599219
you have to solve the ones in the brackets first. so in this instance, 4(-1) = -4.\n\nand then, you solve -4 - 3 = -7