What is (sqrt(3+\sqrt{5)}-sqrt(3-\sqrt{5)})^2 ?

The solution to (sqrt(3+\sqrt{5)}-sqrt(3-\sqrt{5)})^2 is 2

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simplify (sqrt(3+\sqrt{5)}-sqrt(3-\sqrt{5)})^2

simplify

(3 + 5 - 3 - 5)^{2}

2

Solution steps

(3 + 5 - 3 - 5)^{2}

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(3 + 5 - 3 - 5)^{2} = (3 + 5)^{2} - 2 3 + 5 3 - 5 + (3 - 5)^{2}

= (3 + 5)^{2} - 2 3 + 5 3 - 5 + (3 - 5)^{2}

(3 + 5)^{2} - 2 3 + 5 3 - 5 + (3 - 5)^{2} = 6 - 2 3 + 5 3 - 5

= 6 - 2 3 + 5 3 - 5

2 3 + 5 3 - 5 = 4

= 6 - 4

Subtract the numbers:

6 - 4 = 2

= 2

(2 t + \frac{1}{t ^{2}})^{10}

\frac{\frac{1}{3} - 2}{5 + \frac{1}{2}}

8 \cdot 60

8 (sin (x) cos (x))^{2} + cos (4 x)

1 6^{- 2^{- 1}}

What is (sqrt(3+\sqrt{5)}-sqrt(3-\sqrt{5)})^2 ?
The solution to (sqrt(3+\sqrt{5)}-sqrt(3-\sqrt{5)})^2 is 2