hmm... okay, if I understand you correctly, 2 times the square root of 3 times the square root of 12? = 2(1.73)(3.46) = 11.9716. If you aren't using the approximations, then just simplifying is... [sorry, I can't do the square root sign on the computer...] 2(square root of 3)(square root of 12) = 2(square root of 3)(square root of 4*3) = 4(square root of 3)(square root of 3) = 4(3) = 12!!! HOPE I HELPED!! :-)
Square root of 6
square root 6
The square root of 12 equals the square root of 4 times 3. The square root of 4 is 2. The square root of 12 equals 2 times the square root of 3.
Multiply everything by the square root of 3 minus the square root of 2 and then times that by 100 - 72 and divide that by 5
3(3 square root of 2) = 9(square root of 2)
square root 2 times square root 3 times square root 8
1.4142135 is the square root of 2 1.7320508 is the square root of 3 2.0000000 is the square root of 4
2 times the Square root of 3 + 4
hmm... okay, if I understand you correctly, 2 times the square root of 3 times the square root of 12? = 2(1.73)(3.46) = 11.9716. If you aren't using the approximations, then just simplifying is... [sorry, I can't do the square root sign on the computer...] 2(square root of 3)(square root of 12) = 2(square root of 3)(square root of 4*3) = 4(square root of 3)(square root of 3) = 4(3) = 12!!! HOPE I HELPED!! :-)
Square root of 6
2 root 3 over 2, so square root of 3
the square root of 18 can be simplified to 3 * the square root of 2.The perfect square 9 is a factor of 18. That means the square root of 9 * the square root of 2 = the square root of 18.the square root of 9 can be simplified to 3.That leaves 3 * the square root of 2.
sqrt(3) + sqrt(3) = 2*sqrt(3) NOT sqrt(3 + 2)
square root 6
x + y = 1xy = 1y = 1 - xx(1 - x) = 1x - x^2 = 1-x^2 + x - 1 = 0 or multiplying all terms by -1;(-x^2)(-1) + (x)(-1) - (1)(-1) = 0x^2 - x + 1 = 0The roots are complex numbers. Use the quadratic formula and find them:a = 1, b = -1, and c = 1x = [-b + square root of (b^2 - (4)(a)(c)]/2a orx = [-b - square root of (b^2 - (4)(a)(c)]/2aSox = [-(-1) + square root of ((-1)^2 - (4)(1)(1)]/2(1)x = [1 + square root of (1 - 4]/2x = [1 + square root of (- 3)]/2 orx = [1 + square root of (-1 )(3)]/2; substitute (-1) = i^2;x = [1 + square root of (i^2 )(3)]/2x = [1 + (square root of 3)i]/2x = 1/2 + [i(square root of 3]/2 andx = 1/2 - [i(square root of 3)]/2Since we have two values for x, we will find also two values for yy = 1 - xy = 1 - [1/2 + (i(square root of 3))/2]y = 1 - 1/2 - [i(square root of 3)]/2y = 1/2 - [i(square root of 3)]/2 andy = 1 - [1/2 - (i(square root of 3))/2)]y = 1 - 1/2 + [i(square root of 3))/2]y = 1/2 + [i(square root of 3)]/2Thus, these numbers are:1. x = 1/2 + [i(square root of 3)]/2 and y = 1/2 - [i(square root of 3)]/22. x = 1/2 - [i(square root of 3)]/2 and y = 1/2 + [i(square root of 3)]/2Let's check this:x + y = 11/2 + [i(square root of 3)]/2 +1/2 - [i(square root of 3)]/2 = 1/2 + 1/2 = 1xy = 1[1/2 + [i(square root of 3)]/2] [1/2 - [i(square root of 3)]/2]= (1/2)(1/2) -(1/2)[i(square root of 3)]/2] + [i(square root of 3)]/2](1/2) - [i(square root of 3)]/2] [i(square root of 3)]/2]= 1/4 - [i(square root of 3)]/4 + [i(square root of 3)]/4 - (3i^2)/4; substitute ( i^2)=-1:= 1/4 - [(3)(-1)]/4= 1/4 + 3/4= 4/4=1In the same way we check and two other values of x and y.
The square root of 12 equals the square root of 4 times 3. The square root of 4 is 2. The square root of 12 equals 2 times the square root of 3.