Question

(4radical3+5radical2)^2= ?

Answer 1

${(4 \sqrt{3} + 5 \sqrt{2} )}^{2} = {(4 \sqrt{3} ) }^{2} + 2 \times 4 \sqrt{3} \times 5 \sqrt{2} + {(5 \sqrt{2} )}^{2}$

$= {4}^{2} \times 3 + (2 \times 4 \times 5) \sqrt{3 \times 2} + {5}^{2} \times 2$

$= 16 \times 3 + 40 \sqrt{6} + 25 \times 2$

$= 48 + 40 \sqrt{6} + 50$

$= 98 + 40 \sqrt{6}$

$= 2(49 + 20 \sqrt{6} )$

Answer 2

( 4√3 + 5√2 )² = 16×3 + 40√6 + 25×2 = 48 + 40√6 + 50 = 98 + 40√6 = 2(49+20√6)