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

The solution to (sqrt(2+\sqrt{3)}+sqrt(2-\sqrt{3)})^2 is 6

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

simplify

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

6

Solution steps

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

Apply Perfect Square Formula:

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

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

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

(2 + 3)^{2} + 2 2 + 3 2 - 3 + (2 - 3)^{2} = 4 + 2 2 + 3 2 - 3

= 4 + 2 2 + 3 2 - 3

2 2 + 3 2 - 3 = 2

= 4 + 2

Add the numbers:

4 + 2 = 6

= 6

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What is (sqrt(2+\sqrt{3)}+sqrt(2-\sqrt{3)})^2 ?
The solution to (sqrt(2+\sqrt{3)}+sqrt(2-\sqrt{3)})^2 is 6