Question

How do you evaluate `(7-\sqrt{11})(7+\sqrt{11})`?

Answer 1

See a solution process below:

Explanation:

Use this rule for quadratics to evaluate or expand the expression:

`(color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y)) = color(red)(x)^2 - color(blue)(y)^2`

Substitute `7` for `color(red)(x)`

Substitute `sqrt(11)` for `color(blue)(y)`

Giving:

`(color(red)(7) + color(blue)(sqrt(11)))(color(red)(7) - color(blue)(sqrt(11))) = color(red)(7)^2 - (color(blue)(sqrt(11)))^2 = 49 - 11 = 38`