How do you simplify ${(5 + 2 \sqrt{7})}^{2}$ $(5 + 2sqrt7)^2$ ?

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How do you simplify ${(5 + 2 \sqrt{7})}^{2}$ $(5 + 2sqrt7)^2$ ?

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Answer 1 · 2017-08-08T01:50:00

See a solution process below:

Explanation:

We can use this rule to simplify the expression:

${(x + y)}^{2} = x^{2} + 2 x y + y^{2}$ $(color(red)(x) + color(blue)(y))^2 = color(red)(x)^2 + 2color(red)(x)color(blue)(y) + color(blue)(y)^2$

Substituting $5$ $color(red)(5)$ for $x$ $color(red)(x)$ and substituting $2 \sqrt{7}$ $color(red)(2sqrt(7))$ for $y$ $color(blue)(y)$ gives:

${(5 + y)}^{2} \Rightarrow 5^{2} + (2 \cdot 5 \cdot 2 \sqrt{7}) + {(2 \sqrt{7})}^{2} \Rightarrow$ $(color(red)(5) + color(blue)(y))^2 => color(red)(5)^2 + (2 * color(red)(5) * color(blue)(2sqrt(7))) + color(blue)((2sqrt(7)))^2 =>$

$25 + 20 \sqrt{7} + (4 \cdot 7) \Rightarrow$ $25 + 20sqrt(7) + (4 * 7) =>$

$25 + 20 \sqrt{7} + 28 \Rightarrow$ $25 + 20sqrt(7) + 28 =>$

$25 + 28 + 20 \sqrt{7} \Rightarrow$ $25 + 28 + 20sqrt(7) =>$

$53 + 20 \sqrt{7}$ $53 + 20sqrt(7)$

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How do you simplify ${(5 + 2 \sqrt{7})}^{2}$ $(5 + 2sqrt7)^2$ ?

1 Answer

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How do you simplify (5+2√7)2(5 + 2sqrt7)^2?

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How do you simplify ${(5 + 2 \sqrt{7})}^{2}$ $(5 + 2sqrt7)^2$ ?