simplify √(75 ÷ 2) - √(3 ÷ 2)

If you can't simplify it, then please say so.

Simplify the following:
sqrt(75/2)-sqrt(3/2)

sqrt(3/2) = (sqrt(3))/(sqrt(2)):
sqrt(75/2)-(sqrt(3))/(sqrt(2))

Rationalize the denominator. (sqrt(3))/(sqrt(2)) = (sqrt(3))/(sqrt(2))×(sqrt(2))/(sqrt(2)) = (sqrt(3) sqrt(2))/(2):
sqrt(75/2)-(sqrt(3) sqrt(2))/(2)

sqrt(3) sqrt(2) = sqrt(3×2):
sqrt(75/2)-(sqrt(3×2))/(2)

3×2 = 6:
sqrt(75/2)-( sqrt(6 ) )/(2)

sqrt(75/2) = (sqrt(75))/(sqrt(2)):
(sqrt(75))/(sqrt(2))-(sqrt(6))/(2)

sqrt(75) = sqrt(3×5^2) = 5 sqrt(3):
(5 sqrt(3))/(sqrt(2))-(sqrt(6))/(2)

Rationalize the denominator. (5 sqrt(3))/(sqrt(2)) = (5 sqrt(3))/(sqrt(2))×(sqrt(2))/(sqrt(2)) = (5 sqrt(3) sqrt(2))/(2):
(5 sqrt(3) sqrt(2))/(2)-(sqrt(6))/(2)

sqrt(3) sqrt(2) = sqrt(3×2):
(5 sqrt(3×2))/(2)-(sqrt(6))/(2)

3×2 = 6:
(5 sqrt(6 ) )/(2)-(sqrt(6))/(2)

(5 sqrt(6))/(2)-(sqrt(6))/(2) = (5 sqrt(6)-sqrt(6))/(2):
(5 sqrt(6)-sqrt(6))/(2)

5 sqrt(6)-sqrt(6) = 4 sqrt(6):
(4 sqrt(6))/(2)

4/2 = (2×2)/2 = 2:
Answer: | 2 sqrt(6)

$\sqrt{\dfrac{75}{2}}-\sqrt{\dfrac{3}{2}}\\=\dfrac{\sqrt{75}}{\sqrt{2}}-\dfrac{\sqrt{3}}{\sqrt{2}}\\ =\dfrac{5\sqrt3}{\sqrt2}-\dfrac{\sqrt3}{\sqrt2}\\=\dfrac{4\sqrt3}{\sqrt2}\\=\dfrac{2\cdot\sqrt2\cdot\sqrt2\cdot\sqrt3}{\sqrt2}\\ =2\sqrt2\cdot\sqrt3\\ =2\sqrt6$

$\text{Questions:}\\ \text{1. Why is sqrt 75 = 5 sqrt 3?}\\ \text{sqrt 75 = sqrt 25 x sqrt 3 = 5 sqrt 3}\\ $