Question

Simplifique as expressões.

a) -√54-√486-√294
b) √128+√50-√98+√242
c) √396-√108+√176+√675

Answer 1

a)
$- \sqrt{54}- \sqrt{486}- \sqrt{294}=\\- \sqrt{2.3.3^2}- \sqrt{2.3.3^2.3^2}- \sqrt{2.3.7^2}=\\-3 \sqrt{2.3}-3.3 \sqrt{2.3}-7 \sqrt{2.3}=\\-3 \sqrt{6}-9 \sqrt{6}-7 \sqrt{6}=\\(-3-9-7) \sqrt{6} =\\-19\sqrt{6}$

b)
$\sqrt{128}+ \sqrt{50}- \sqrt{98}+ \sqrt{242}=\\ \sqrt{2^2.2^2.2^2.2}+ \sqrt{2.5^2}- \sqrt{2.7^2}+ \sqrt{2.11^2}=\\2^3 \sqrt{2}+5 \sqrt{2}-7 \sqrt{2}+11\sqrt{2}=\\(8+5-7+11) \sqrt{2}=\\17\sqrt{2}$

c)
$\sqrt{396}- \sqrt{108}+ \sqrt{176}+ \sqrt{675}=\\ \sqrt{2^2.3^2.11}- \sqrt{2^2.3^2.3}+ \sqrt{2^2.2^2.11}+ \sqrt{3^2.5^2.3}=\\2.3 \sqrt{11}-2.3 \sqrt{3}+2^2 \sqrt{11}+3.5 \sqrt{3}=\\6 \sqrt{11}-6 \sqrt{3}+4 \sqrt{11}+15 \sqrt{3}=\\6 \sqrt{11}+4 \sqrt{11}-6 \sqrt{3}+15 \sqrt{3}=\\(6+4)\sqrt{11}(-6+15)\sqrt{3}=\\10\sqrt{11} +9\sqrt{3}$