Question

5) Simplifique:
a) √20 - √24 + √125 - √54 =
b) √16 elevado a 3 + √ 54 elevado a 3 / √125 elevado a 3 =

ME AJUDEM POR FAVORRR

Answer 1

Resposta:

5)

a)

$\sqrt{20} - \sqrt{24} + \sqrt{125} - \sqrt{54} = \\ \\ \sqrt{4 \times 5} - \sqrt{4 \times 6} + \sqrt{ 25 \times 5} - \sqrt{9 \times 6} = \\ \\ \sqrt{4} \times \sqrt{5} - \sqrt{4} \times \sqrt{6} + \sqrt{25} \times \sqrt{5} - \sqrt{9} \times \sqrt{6} = \\ \\ \orange{2 \sqrt{5} } - 2 \sqrt{6} \orange{+ 5 \sqrt{5} } - 3 \sqrt{6} = \\ \\ \green{7 \sqrt{5} - 5 \sqrt{6} }$

b)

$\dfrac{( \sqrt{16} ) {}^{3} + ( \sqrt{54)} {}^{3} }{( \sqrt{125)} {}^{3} } = \\ \\ \dfrac{ {4}^{3} + ( \sqrt{9 \times 6} ) {}^{3} }{ (\sqrt{ {5}^{3} }) {}^{3} } = \\ \\ \dfrac{64 + \sqrt{ {9}^{3} \times {6}^{3} } }{5} = \\ \\ \dfrac{64 + \sqrt{9 {}^{2} \times 9 \times {6}^{2} \times 6 } }{5} = \\ \\ \dfrac{64 + 9 \times 3 \times 6 \sqrt{6} }{5} \\ \\ \pink{\dfrac{64 + 162 \sqrt{6} }{5} }$

Bons Estudos!