Question

Dê o resultado de cada expressão: ( simplifique se necessário)
A) √20 + √45 =
B) 3√5 - 10 √5 =
C) 4 √10 . 3 √20 =
D) √30 ÷ √5 =

me ajudem​

Answer 1

$\Large\boxed{\begin{array}{l}\begin{array}{c|c}\sf20&\sf2\\\sf10&\sf2\\\sf5&\sf5\\\sf1\end{array}\\\sf 20=2^2\cdot 5\\\begin{array}{c|c}\sf45&\sf3\\\sf15&\sf3\\\sf5&\sf5\\\sf1\end{array}\\\tt a)~\sf\sqrt{20}+\sqrt{45}=\sqrt{2^2\cdot5}+\sqrt{3^2\cdot5}\\\sf\sqrt{20}+\sqrt{45}=2\sqrt{5}+3\sqrt{5}=5\sqrt{5}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt b)~\sf 3\sqrt{5}-10\sqrt{5}=-7\sqrt{5}\\\tt c)~\sf 4\sqrt{10}\cdot 3\sqrt{20}=12\sqrt{200}\\\begin{array}{c|c}\sf200&\sf2\\\sf100&\sf2\\\sf50&\sf2\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 200=2^2\cdot2\cdot 5^2\\\sf 12\sqrt{200}=12\cdot\sqrt{2^2\cdot2\cdot5^2}\\\sf=12\cdot2\cdot5\sqrt{2}=120\sqrt{2}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt d)~\sf \sqrt{30}\div\sqrt{5}=\sqrt{30\div5}=\sqrt{6}\end{array}}$