`a, 3sqrt((2-sqrt5)^2) - 2sqrt(sqrt5-3)^2)`
`= 3(sqrt 5 - 2) - 2(3 - sqrt 5)`.
`= 3 sqrt 5 - 6 - 6+ 2 sqrt 5`.
`= 5 sqrt 5 - 12.`
`b, 7sqrt((1-sqrt 2)^2) - 4sqrt((sqrt2-3)^2)`
`= 7(sqrt 2 - 1) - 4(3-sqrt 2)`.
`= 7 sqrt 2 - 7 - 12 + 4 sqrt 2`.
`= 11 sqrt 2 - 19`.
`c, sqrt((2-sqrt7)^2) - sqrt((1-sqrt7)^2)`
`= sqrt 7 - 2 - sqrt 7 + 1`
`= -1`.
`d, 4sqrt((4-3sqrt3)^2) - 7sqrt((2sqrt3-1)^2)`
`= 4(3 sqrt 3 - 4) - 7(2sqrt3-1)`
`= 12 sqrt 3 - 16 - 14 sqrt 3 + 7`
`= -2 sqrt 3 - 9`.
a) \(A=3\sqrt{\left(2-\sqrt{5}\right)^2}-2\sqrt{\left(\sqrt{5}-3\right)^2}\)
\(A=3\left|2-\sqrt{5}\right|-2\left|\sqrt{5}-3\right|\)
\(A=3\left(-2+\sqrt{5}\right)-2\left(3-\sqrt{5}\right)\)
\(A=-6+3\sqrt{5}-6+2\sqrt{5}\)
\(A=-12+5\sqrt{5}\)
b) \(B=7\sqrt{\left(1-\sqrt{2}\right)^2}-4\sqrt{\left(\sqrt{2}-3\right)^2}\)
\(B=7\left|1-\sqrt{2}\right|-4\left|\sqrt{2}-3\right|\)
\(B=7\left(-1+\sqrt{2}\right)-4\left(3-\sqrt{2}\right)\)
\(B=-7+7\sqrt{2}-12+4\sqrt{2}\)
\(B=-19+11\sqrt{2}\)
c) \(C=\sqrt{\left(2-\sqrt{7}\right)^2}-\sqrt{\left(1-\sqrt{7}\right)^2}\)
\(C=\left|2-\sqrt{7}\right|-\left|1-\sqrt{7}\right|\)
\(C=-2+\sqrt{7}+1-\sqrt{7}\)
\(C=-1\)
d) \(D=4\sqrt{\left(4-3\sqrt{3}\right)^2}-7\sqrt{\left(2\sqrt{3}-1\right)^2}\)
\(D=4\left|4-3\sqrt{3}\right|-7\left|2\sqrt{3}-1\right|\)
\(D=4\left(-4+3\sqrt{3}\right)-7\left(2\sqrt{3}-1\right)\)
\(D=-16+12\sqrt{3}-14\sqrt{3}+7\)
\(D=-9-2\sqrt{3}\)
