Question

1 Operações com radicais, simplifique os radicais e resolva as operações:

√2 + √32=

3√5 + √20=

√12 - 6√3=

√28 - 10√7=




2-Racionalize o denominador de cada fração:

5/√7



15/√5


me ajudem por favor

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Answer 1

Explicação passo-a-passo:

1)

$\sqrt{2} + \sqrt{32}\\\\=\sqrt{2} + \sqrt{2.16}\\\\=\sqrt{2} + \sqrt{2}\sqrt{16}\\\\=\sqrt{2} + 4\sqrt{2}=5\sqrt{2}$

$3\sqrt{5} + \sqrt{20}\\\\=3\sqrt{5} + \sqrt{4.5}\\\\=3\sqrt{5} + \sqrt{4}\sqrt{5}\\\\=3\sqrt{5} + 2\sqrt{5}\\\\=5\sqrt{5}$

$\sqrt{12} - 6\sqrt{3}\\\\=\sqrt{4.3} - 6\sqrt{3}\\\\=\sqrt{4}\sqrt{3} - 6\sqrt{3}\\\\=2\sqrt{3} - 6\sqrt{3}\\\\=-4\sqrt{3}$

$\sqrt{28} - 40\sqrt{7}\\\\=\sqrt{4.7} - 40\sqrt{7}\\\\=\sqrt{4}\sqrt{7} - 40\sqrt{7}\\\\=2\sqrt{7} - 40\sqrt{7}\\\\= - 38\sqrt{7}$

2)

$\dfrac{5}{\sqrt{7}}\\\\\\=\dfrac{5}{\sqrt{7}}.1\\\\\\=\dfrac{5}{\sqrt{7}}.\dfrac{\sqrt{7}}{\sqrt{7}}\\\\\\=\dfrac{5\sqrt{7}}{\sqrt{7.7}}\\\\\\=\dfrac{5\sqrt{7}}{\sqrt{7^2}}\\\\\\=\dfrac{5\sqrt{7}}{\sqrt{7}^2}\\\\\\=\dfrac{5\sqrt{7}}{7}$

$\dfrac{15}{\sqrt{5}}\\\\\\=\dfrac{15}{\sqrt{5}}.1\\\\\\=\dfrac{15}{\sqrt{5}}.\dfrac{\sqrt{5}}{\sqrt{5}}\\\\\\=\dfrac{15\sqrt{5}}{\sqrt{5.5}}\\\\\\=\dfrac{15\sqrt{5}}{\sqrt{5^2}}\\\\\\=\dfrac{15\sqrt{5}}{\sqrt{5}^2}\\\\\\=\dfrac{15\sqrt{5}}{5}\\\\\\=\dfrac{3.5\sqrt{5}}{5}\\\\\\=3\sqrt{5}$

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