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

The solution to (sqrt(x+\sqrt{y)}+sqrt(x-\sqrt{y)})^2 is 2x+2sqrt(x+\sqrt{y)}sqrt(x-\sqrt{y)}

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simplify (sqrt(x+\sqrt{y)}+sqrt(x-\sqrt{y)})^2

simplify

(x + y + x - y)^{2}

2 x + 2 x + y x - y

Solution steps

(x + y + x - y)^{2}

Apply Perfect Square Formula:

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

(x + y + x - y)^{2} = (x + y)^{2} + 2 x + y x - y + (x - y)^{2}

= (x + y)^{2} + 2 x + y x - y + (x - y)^{2}

Simplify

(x + y)^{2} + 2 x + y x - y + (x - y)^{2} : 2 x + 2 x + y x - y

= 2 x + 2 x + y x - y

\frac{2019 + ln ( x - 1 ) ( x - 1 )}{e ^{x}}

(x + \frac{2}{3})^{3}

\frac{x ^{(2)} + x + 2}{x ^{(2)} ( x ^{(2)} + 3 ) ^{(2)}}

\frac{2 x - x ^{2}}{3 ( 2 - 2 x ) ^{2}}

(3 n - 3) 2

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