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

Question

1681 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-08T01:50:00

See a solution process below:

We can use this rule to simplify the expression:

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

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

$(color(red)(5) + color(blue)(y))^2 => color(red)(5)^2 + (2 * color(red)(5) * color(blue)(2sqrt(7))) + color(blue)((2sqrt(7)))^2 =>$

$25 + 20sqrt(7) + (4 * 7) =>$

$25 + 20sqrt(7) + 28 =>$

$25 + 28 + 20sqrt(7) =>$

$53 + 20sqrt(7)$

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