Question

(√2 + √3)^2 =
(√7 + √3)^2 =
(11 − √7)^2 =

;-;

Answer 1

Explicação passo-a-passo:

$( \sqrt{2} + \sqrt{3} {)}^{2} = ( \sqrt{2} {)}^{2} + 2 \sqrt{2} \sqrt{3} + ( \sqrt{3} {)}^{2}$

$= 2 + 2 \sqrt{2 \times 3} + 3$

$= 5 + 2 \sqrt{6}$

$( \sqrt{7} + \sqrt{3} {)}^{2} = ( \sqrt{7} {)}^{2} + 2 \sqrt{7} \sqrt{3} + ( \sqrt{3} {)}^{2}$

$= 7 + 2 \sqrt{7 \times 3} + 3$

$= 10 + 2 \sqrt{21}$

$( \sqrt{11} - \sqrt{7} {)}^{2} = ( \sqrt{11} {)}^{2} - 2 \sqrt{11} \sqrt{7} + ( \sqrt{7} {)}^{2}$

$= 11 + 2 \sqrt{11 \times 7} + 7$

$= 18 + 2 \sqrt{77}$