Question

1) simplifique os radicais e efetue as operações ​

Answer 1

a)

$\sqrt{2} + \sqrt{32} + \sqrt{8} = \\ \sqrt{2} + \sqrt{2 {}^{2} + 2 {}^{2} + 2 } + \sqrt{2 {}^{2} + 2 } = \\ \sqrt{2} + 2.2 \sqrt{2} + 2 \sqrt{2} = \\ \sqrt{2} + 4 \sqrt{2} + 2 \sqrt{2} = 7 \sqrt{2}$

b)

$3 \sqrt{5} + \sqrt{2 {}^{2} + 5} + \sqrt{3 {}^{2} + 5} = \\ 3\sqrt{5} + 2 \sqrt{5} + 3 \sqrt{5} = 8 \sqrt{5}$

c)

$\sqrt{2 {}^{2} + 7} - 10\sqrt{7} + 5\sqrt{7} = 2 \sqrt{7} - 10 \sqrt{7} + 5 \sqrt{7} = - 3 \sqrt{7}$

d)

$\sqrt{2 {}^{2} + 3} - 6\sqrt{3} + \sqrt{5 {}^{2} + 3} = \\ 2 \sqrt{3} - 6 \sqrt{3} + 5 \sqrt{3} = \sqrt{3}$

e)

$9 \sqrt{2} + 3 \sqrt{5 {}^{2} + 2 } = 9\sqrt{2} + 3.5 \sqrt{2} = 9\sqrt{2} + 15 \sqrt{2} = 24 \sqrt{2}$

f)

$\sqrt{7 {}^{2} + 2 } - \sqrt{3 {}^{2} + 2} - 5 \sqrt{2 {}^{2} + 2 {}^{2} + 2 } = 7 \sqrt{2} - 3 \sqrt{2} - 5.2.2 \sqrt{2} = 7\sqrt{2} - 3 \sqrt{2} - 20 \sqrt{2}$