1003118203 Level: CAssuming \( 12 < \sqrt{153} < 13 \), which interval does the number \( \frac{5-\sqrt{153}}5 \) belong to? Do not use a calculator.\( (-1.6; -1.4 ) \)\( (-1.8; -1.5 ) \)\( (1.4; 1.6 ) \)\( (1.6; 1.8 ) \)
1003118202 Level: CThe approximate value of the number \( 10^{-0.8} \) is \( 0.158489 \). What is the approximate value of the number \( 10^{1.2} \)? Give your answer to three decimal places. Do not use a calculator.\( 15.849 \)\( 1.585 \)\( 0.015 \)\( 3.170 \)
1003118201 Level: CSuppose that \( \sqrt[3]2\approx 1.25 \). Give the approximate value of \( \left(\frac1{81}\right)^{-\sqrt[3]2}\). Do not use a calculator.\( 243 \)\( 729 \)\( \frac19 \)\( 0 \)
1003118110 Level: CLet \( \frac{u\sqrt5}{5-\sqrt5}=\frac{\frac{5+\sqrt5}{\sqrt5+1}}{1-\sqrt5} \). What is the reciprocal of \( u \)?\( \frac1u=-\frac{\sqrt5}5 \)\( \frac1u = \frac1{\sqrt5} \)\( \frac1u = \frac5{\sqrt5} \)\( \frac1u = -\sqrt5 \)
1003118109 Level: CWhich of the following numbers has the same unit digit as the number \( 555^{555} \)?\( 10^{555}+5 \)\( \frac{10^{555}}5 \)\( 5\cdot10^{555} \)\( 10^{555}+10^{555} \)
1003118108 Level: CThe value of \( \sqrt{5\left(222^2+111^2\right)} \) is:\( 555 \)\( 111\sqrt5 \)\( \sqrt{15} \)\( \sqrt{1110^2-555^2} \)
1003118107 Level: BThe number \( \left(\frac{27^{-4}\cdot8^{-4}}{16^{-2}\cdot9^{-5}}\right)^{-3} \) equals:\( 12^{6} \)\( 6^6 \)\( 6^{12} \)\( \frac1{3^6\cdot2^{12}} \)
1003118105 Level: CThe number \( \frac1{\left(2-\sqrt3\right)^3} \) is equal to:\( 26+15\sqrt3 \)\( 27+24\sqrt3 \)\( 14+7\sqrt3 \)\( 27+30\sqrt3 \)
1003118104 Level: CSimplify \(\sqrt[4]{\left(\sqrt3-\sqrt2\right)^4}+\sqrt[4]{\left(\sqrt2-\sqrt5\right)^4}+\sqrt[3]{\left(\sqrt3-\sqrt5\right)^3} \).\( 2\sqrt3-2\sqrt2 \)\( 2\sqrt5 - 2\sqrt2 \)\( 2\sqrt3-2\sqrt5 \)\( 2\sqrt5-2\sqrt3 \)
1003118103 Level: BExpress \( \frac{\sqrt[3]5\sqrt[6]5}{3\cdot25^3+2\cdot125^2} \) as a power of \( 5 \).\( 5^{-\frac{13}2} \)\( 5^{-5} \)\( 5^{-6} \)\( 5^{-\frac{11}2} \)