Maths

(√6 - √2)/4 =?

can't be simplified

 

 

√(2 - √3)/2 (6 - 2√12 + 2)/16 =?

\(\frac{\sqrt{(2 - \sqrt3)}}{2}\times \frac{ (6 - 2\sqrt{12} + 2)}{16} \\ =\frac{\sqrt{(2 - \sqrt3)}}{2}\times \frac{ (8 - 2\sqrt{12} )}{16} \\ =\frac{\sqrt{(2 - \sqrt3)}}{1}\times \frac{ (4 - \sqrt{12} )}{16} \\ =\frac{\sqrt{(2 - \sqrt3)}}{1}\times \frac{ (4 - 2\sqrt{3} )}{16} \\ =\frac{\sqrt{(2 - \sqrt3)}}{1}\times \frac{ (2 - \sqrt{3} )}{8} \\ =\frac{(2 - \sqrt3)^{0.5}}{1}\times \frac{ (2 - \sqrt{3} )}{8} \\ =\frac{(2 - \sqrt3)^{1.5}}{8} \qquad or\\ =\left(\frac{2 - \sqrt3}{4}\right)^{1.5} \\\)

 

 

 

(2 - √3)/4 8 - 4√3 =?

 

\(\frac{(2 - \sqrt3)}{4 8} - 4\sqrt 3 \\ =\frac{(2 - \sqrt3)-4*48\sqrt3}{4 8} \\ =\frac{2 - \sqrt3-192\sqrt3}{4 8} \\ =\frac{2 -193\sqrt3}{4 8} \\ \)

 

 

4(2 - √3) 8 - 4√3 = 8 - 4√3

 

\(4(2 - \sqrt3) 8 - 4√3 = 8 - 4\sqrt3\)

 

This doesn't make sense.

(2 - √3)/4 8 - 4√3 =?

 

Simplify the following:
((2-sqrt(3))×8)/(4)-4 sqrt(3)

8/4 = (4×2)/4 = 2:
2 (2-sqrt(3))-4 sqrt(3)

Expand 2 (2-sqrt(3)), resulting in 4-2 sqrt(3):
4-2 sqrt(3)-4 sqrt(3)

Add like terms. 4-2 sqrt(3)-4 sqrt(3)  =  4-6 sqrt(3):
4-6 sqrt(3)

Factor 2 out of 4-6 sqrt(3) giving 2 (2-3 sqrt(3)):
Answer: |  2 (2-3 sqrt(3))

4(2 - √3) 8 - 4√3=?

 

Simplify the following:
4 (2-sqrt(3))×8-4 sqrt(3)

4×8  =  32:
32 (2-sqrt(3))-4 sqrt(3)

Expand 32 (2-sqrt(3)), resulting in 64-32 sqrt(3):
64-32 sqrt(3)-4 sqrt(3)

Add like terms. 64-32 sqrt(3)-4 sqrt(3)  =  64-36 sqrt(3):
64-36 sqrt(3)

Factor 4 out of 64-36 sqrt(3) giving 4 (16-9 sqrt(3)):
Answer: |  4 (16-9 sqrt(3))