Question

5) Sejam a= raiz de 2000 + raiz de 500 e b=36 + raiz de 45.Escreva a+b de maneira simplificada

Answer 1

Explicação passo-a-passo:

$\sqrt{2000}=\sqrt{400\cdot5}=20\sqrt{5}$

$\sqrt{500}=\sqrt{100\cdot5}=10\sqrt{5}$

$a=\sqrt{2000}+\sqrt{500}=20\sqrt{5}+10\sqrt{5}=30\sqrt{5}$

$\sqrt{45}=\sqrt{9\cdot5}=3\sqrt{5}$

$b=36+\sqrt{45}=36+3\sqrt{5}$

$a+b=30\sqrt{5}+36+3\sqrt{5}$

$a+b=36+33\sqrt{5}$

$a+b=3\cdot(12+11\sqrt{5})$