11. Nilai dari \( \left (\sqrt{27} - \sqrt{125}\right )\left (\sqrt{3} + \sqrt{20}\right ) = \) ......
a) \( -\sqrt{15} - 41 \)
b) \( \sqrt{15} - 41 \)
c) \( -3\sqrt{15} - 23 \)
d) \( 3\sqrt{15} - 41 \)
e) \( \sqrt{15} - 23 \)
Penyelesaian :
\( \sqrt{81} + \sqrt{540} - \sqrt{375} - \sqrt{2.500} \)
\( 9 + \sqrt{36\times15} - \sqrt{25\times15} - 50 \)
\( 9 + 6\sqrt{15} - 5\sqrt{15} - 50 \)
\( \sqrt{15} - 41 \)
12. Nilai dari \( \left (4 + 3\sqrt{2}\right )^{2}\left (4 - 3\sqrt{2}\right ) = \) ....
a) \( -136 - 102\sqrt{2} \)
b) \( -40 - 60\sqrt{2} \)
c) \( -8 - 6\sqrt{2} \)
d) \( 8 + 6\sqrt{2} \)
e) \( 136 + 102\sqrt{2} \)
Penyelesaian :
\( \left (4 + 3\sqrt{2}\right )\left (4 + 3\sqrt{2}\right ) \)
\( 16 + 12\sqrt{2} + 12\sqrt{2} + 18 \)
\( \left (34 + 24\sqrt{2}\right )\left (4 - 3\sqrt{2}\right ) \)
\( 136 - 102\sqrt{2} + 96\sqrt{2} - 144 \)
\( -8 - 6\sqrt{2} \)
13. Hasil dari \( \left (\sqrt{2} + \sqrt{3} - \sqrt{6}\right )^{2} - \left (\sqrt{2} - \sqrt{3} + \sqrt{6}\right )^{2} = \).........
a) \( 2\sqrt{6}\left (1 - \sqrt{2}\right ) \)
b) \( 4\sqrt{6}\left (1 - \sqrt{3}\right ) \)
c) \( 4\sqrt{6}\left (1 - \sqrt{2}\right ) \)
d) \( 48 - 25\sqrt[3]{16} \)
e) \( 4\sqrt{6}\left (1 + \sqrt{2}\right ) \)
Penyelesaian :
\( \left (\sqrt{2} + \sqrt{3} - \sqrt{6}\right )\left (\sqrt{2} + \sqrt{3} - \sqrt{6}\right ) - \left (\sqrt{2} - \sqrt{3} + \sqrt{6}\right )\left (\sqrt{2} - \sqrt{3} + \sqrt{6}\right ) \)
\( \left (2 + \sqrt{6} - \sqrt{12} + \sqrt{6} + 3 - \sqrt{18} - \sqrt{12} - \sqrt{18} + 6\right ) - \left (2 - \sqrt{6} + \sqrt{12} - \sqrt{6} + 3 - \sqrt{18} + \sqrt{12} - \sqrt{18} + 6\right ) \)
\( \left (11 + 2\sqrt{6} - 4\sqrt{3} - 6\sqrt{2}\right ) - \left (11 - 2\sqrt{6} + 4\sqrt{3} - 6\sqrt{2}\right ) \)
\( 4\sqrt{6} - 8\sqrt{3} = 2\sqrt{6}\left (1 - \sqrt{2}\right ) \)
14. Nilai dari \( \sqrt[3]{25} \times \sqrt[3]{0,2} \times \sqrt[3]{3.125} = \) .........
a) \( 6 \)
b) \( 7 \)
c) \( 10 \)
d) \( 15 \)
e) \( 25 \)
Penyelesaian :
\( \sqrt[3]{25\times0,2\times3.125} \)
\( \sqrt[3]{15.625} \)
\( 25 \)
15. \( \sqrt[5]{\frac{1}{243}} + \sqrt[3]{\sqrt{729}} + \sqrt{\sqrt[3]{\frac{1}{64}}} = \) .........
a) \( 5\frac{1}{3} \)
b) \( 4\frac{2}{3} \)
c) \( 3\frac{2}{5} \)
d) \( 3\frac{5}{6} \)
e) \( 3 \)
Penyelesaian :
\( \sqrt[5]{\frac{1}{243}} = \frac{1}{3} \)
\( \sqrt[3]{27} = 3 \)
\( \left (\left (\frac{1}{64}\right )^{\frac{1}{3}}\right )^{\frac{1}{2}} = \left (\frac{1}{64}\right )^{\frac{1}{6}} = \sqrt[6]{\frac{1}{64}} = \frac{1}{2} \)
\( \frac{1}{3} + 3 + \frac{1}{2} \)
\( 3\frac{5}{6} \)
16. \( 54\sqrt{40} : 9\sqrt{24} = \) ......
a) \( 2\sqrt{15} \)
b) \( 3\sqrt{15} \)
c) \( 4\sqrt{15} \)
d) \( 3\sqrt{6} \)
e) \( 6\sqrt{6} \)
Penyelesaian :
\( 54\sqrt{4\times10} : 9\sqrt{4\times6} \)
\( \frac{108\sqrt{10}}{18\sqrt{6}} \)
\( \frac{6\sqrt{10}}{\sqrt{6}}\times\frac{\sqrt{6}}{\sqrt{6}} = \frac{6\sqrt{60}}{6} = \sqrt{60} \)
\( \sqrt{4\times15} \)
\( 2\sqrt{15} \)
17. Jika \( p = 3\sqrt{2} - 5\sqrt{3} \) dan \( q = \sqrt{2} + 5\sqrt{3} \) , maka nilai dari \( p^{2} - q^{2} = \) .......
a) \( -69 \)
b) \( 16 \)
c) \( 16 - 10\sqrt{6} \)
d) \( 16 - 14\sqrt{6} \)
e) \( 16 - 40\sqrt{6} \)
Penyelesaian :
\( \left (3\sqrt{2} - 5\sqrt{3}\right )^{2} - \left (\sqrt{2} + 5\sqrt{3}\right )^{2} \)
\( \left (18 - 30\sqrt{6} + 75\right ) - \left (2 + 10\sqrt{6} + 75\right ) \)
\( 93 - 30\sqrt{6} - 77 - 10\sqrt{6} \)
\( 16 - 40\sqrt{6} \)
18. Jika \( a = 3 + 2\sqrt{5} \) dan \( b = 3 - 2\sqrt{5} \) , maka \( 4ab - \left (a + b\right )^{4} = \) ......
a) \( -1.620 \)
b) \( -1.340 \)
c) \( -1.300 \)
d) \( -1.252 \)
e) \( 1. 292 \)
Penyelesaian :
\( 4\left (3 + 2\sqrt{5}\right )\left (3 - 2\sqrt{5}\right ) - \left (3 + 2\sqrt{5} + 3 - 2\sqrt{5}\right )^{4} \)
\( 4\left (3 + 2\sqrt{5}\right )\left (3 - 2\sqrt{5}\right ) - \left (6\right )^{4} \)
\( 4\left( 9 - 6\sqrt{5} + 6\sqrt{5} - 4\sqrt{25}\right) - 1.296 \)
\( 36 - 16\sqrt{25} - 1.296 \)
\( 36 - 80 - 1.296 \)
\( -1.340 \)
19. Jika \( p = 5 + \sqrt{6} \) , \( q = \sqrt{3} - \sqrt{2} \) dan \( r = 2\sqrt{3} - 3\sqrt{2} \) , maka \( pqr = \)....
a) \( 6 + 3\sqrt{6} \)
b) \( 18 - 3\sqrt{6} \)
c) \( 30 - 13\sqrt{6} \)
d) \( 18 + 3\sqrt{6} \)
e) \( 20 + 13\sqrt{6} \)
Penyelesaian :
\( \left ( 5 + \sqrt{6} \right )\left ( \sqrt{3} - \sqrt{2} \right )\left ( 2\sqrt{3} - 3\sqrt{2} \right ) \)
\( \left ( 5\sqrt{3} - 5\sqrt{2} + \sqrt{18} - \sqrt{12} \right )\left ( 2\sqrt{3} - 3\sqrt{2} \right ) \)
\( \left ( 3\sqrt{3} - 2\sqrt{2} \right )\left ( 2\sqrt{3} - 3\sqrt{2} \right ) \)
\( 6\sqrt{9} - 9\sqrt{6} - 4\sqrt{6} + 6\sqrt{4} \)
\( 18 - 13\sqrt{6} + 12 \)
\( 30 - 13\sqrt{6} \)
20. \( \frac{\sqrt{48} - 2\sqrt{18} + \sqrt{75} + 4\sqrt{50} - \sqrt{27}}{\sqrt{125} + 2\sqrt{169} + \sqrt{45} - 4\sqrt{20} - \sqrt{576}} = \)....
a) \( 6\sqrt{3} + 14\sqrt{2} \)
b) \( 6\sqrt{3} + 14 \)
c) \( 6\sqrt{3} + 7\sqrt{2} \)
d) \( 3\sqrt{3} + 14\sqrt{2} \)
e) \( 3\sqrt{3} + 7\sqrt{2} \)
Penyelesaian :
\( \frac{4\sqrt{3} - 6\sqrt{2} + 5\sqrt{3} + 20\sqrt{2} - 3\sqrt{3}}{5\sqrt{5} + 26 + 3\sqrt{5} - 8\sqrt{5} - 24} \)
\( \frac{6\sqrt{3} + 14\sqrt{2}}{2} \)
\( 3\sqrt{3} + 7\sqrt{2} \)
