Question

Efetuar as operações:

a) ( 2√5 - 4√7) . (√5 + 2 √7)

b) (4 - √5)²

c) ( 1 - √2)⁴

d) (√20 - √45 + 3√125) : 2√5

Answer 1

$a)(2 \sqrt{5} -4 \sqrt{7}) ( \sqrt{5} +2 \sqrt{7})=2.5 +4 \sqrt{35}-4\sqrt{35} -8.7=10-56=-4 \\ \\ b)(4- \sqrt{5} )^2=4^2-2.4. \sqrt{5} +( \sqrt{5} )^2=16-8 \sqrt{5} +5=21-8 \sqrt{5} \\ \\ c)(1- \sqrt{2} )^4=[(1- \sqrt{2} )^2]^2=[(1^2-2.1. \sqrt{2}+( \sqrt{2} )^2 )]^2= \\ {(1-2 \sqrt{2}+2 )}^2=(3-2 \sqrt{2} )^2=3^2-2.3.2 \sqrt{2} +(2 \sqrt{2})^2 \\ 9-12 \sqrt{2} +4.2=17-12 \sqrt{2}$$a)(2 \sqrt{5} -4 \sqrt{7}) ( \sqrt{5} +2 \sqrt{7})=2.5 +4 \sqrt{35}-4\sqrt{35} -8.7=10-56=-4 \\ \\ b)(4- \sqrt{5} )^2=4^2-2.4. \sqrt{5} +( \sqrt{5} )^2=16-8 \sqrt{5} +5=21-8 \sqrt{5} \\ \\ c)(1- \sqrt{2} )^4=[(1- \sqrt{2} )^2]^2=[(1^2-2.1. \sqrt{2}+( \sqrt{2} )^2 )]^2= \\ {(1-2 \sqrt{2}+2 )}^2=(3-2 \sqrt{2} )^2=3^2-2.3.2 \sqrt{2} +(2 \sqrt{2})^2 \\ 9-12 \sqrt{2} +4.2=17-12 \sqrt{2}$