16.
a)
[tex]6 \sqrt{7} + 2(3 - 2 \sqrt{7} ) = 6 \sqrt{7} + 6 - 4 \sqrt{7} = 2 \sqrt{7} + 6[/tex]
b)
[tex]3 - 2 \sqrt{5} - (4 \sqrt{5} - 6) = 3 - 2 \sqrt{5} - 4 \sqrt{5} + 6 = 9 - 6 \sqrt{5} [/tex]
c)
[tex] - 3 \sqrt{6} - 3(1 - 2 \sqrt{6} ) = - 3 \sqrt{6} - 3 + 6 \sqrt{6} = 3 \sqrt{6} - 3[/tex]
d)
[tex]5(2 + 4 \sqrt{3} ) + 2( \sqrt{3} - 5) = 10 + 20 \sqrt{3} + 2 \sqrt{3} - 10 = 22 \sqrt{3} [/tex]
e)
[tex]3(2 - \sqrt[3]{2} ) - (5 \sqrt[3]{2} + 4) = 6 - 3 \sqrt[3]{2} - 5 \sqrt[3]{2} - 4 = 2 - 8 \sqrt[3]{2} [/tex]
f)
[tex] - 2(5 - \sqrt[3]{7} ) - 3(2 \sqrt[3]{7} + 3) = - 10 + 2 \sqrt[3]{7} - 6 \sqrt[3]{7} - 9 = - 19 - 4 \sqrt[3]{7} [/tex]
17.
a)
[tex] \sqrt{( \frac{3}{7} {)}^{2} } = \frac{3}{7} [/tex]
b)
[tex]( \sqrt{13} {)}^{2} = 13[/tex]
c)
[tex] \sqrt{15} \times \sqrt{15} = ( \sqrt{15} {)}^{2} = 15[/tex]
d)
[tex]( \sqrt{1.3} {)}^{2} = 1.3[/tex]
e)
[tex] \sqrt[3]{ {5}^{3} } = 5[/tex]
f)
[tex]( \sqrt[3]{7} {)}^{3} = 7[/tex]
g)
[tex] \sqrt[3]{9} \times \sqrt[3]{9} \times \sqrt[3]{9} = ( \sqrt[3]{9} {)}^{3} = 9[/tex]
h)
[tex]( - \sqrt[3]{2} {)}^{3} = - 2[/tex]
