What is (sqrt(x-5)+8)^2 ?

The solution to (sqrt(x-5)+8)^2 is x+16sqrt(x-5)+59

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simplify (sqrt(x-5)+8)^2

simplify

(x - 5 + 8)^{2}

x + 16 x - 5 + 59

Solution steps

(x - 5 + 8)^{2}

Apply Perfect Square Formula:

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

(x - 5 + 8)^{2} = (x - 5)^{2} + 2 x - 5 \cdot 8 + 8^{2}

= (x - 5)^{2} + 2 x - 5 \cdot 8 + 8^{2}

Simplify

(x - 5)^{2} + 2 x - 5 \cdot 8 + 8^{2} : x + 16 x - 5 + 59

= x + 16 x - 5 + 59

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