What is expand (x^{1/2}+y^{1/2})^2 ?

The solution to expand (x^{1/2}+y^{1/2})^2 is x+2x^{1/2}y^{1/2}+y

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expand (x^{1/2}+y^{1/2})^2

expand

(x^{\frac{1}{2}} + y^{\frac{1}{2}})^{2}

x + 2 x^{\frac{1}{2}} y^{\frac{1}{2}} + y

Solution steps

(x^{\frac{1}{2}} + y^{\frac{1}{2}})^{2}

Apply Perfect Square Formula:

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

(x^{\frac{1}{2}} + y^{\frac{1}{2}})^{2} = (x^{\frac{1}{2}})^{2} + 2 x^{\frac{1}{2}} y^{\frac{1}{2}} + (y^{\frac{1}{2}})^{2}

= (x^{\frac{1}{2}})^{2} + 2 x^{\frac{1}{2}} y^{\frac{1}{2}} + (y^{\frac{1}{2}})^{2}

(x^{\frac{1}{2}})^{2} = x

(y^{\frac{1}{2}})^{2} = y

= x + 2 x^{\frac{1}{2}} y^{\frac{1}{2}} + y

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What is expand (x^{1/2}+y^{1/2})^2 ?
The solution to expand (x^{1/2}+y^{1/2})^2 is x+2x^{1/2}y^{1/2}+y