1003158603
Level:
C
After rationalizing the denominator \( \frac{\sqrt{\sqrt{13}+\sqrt{12}}}{\sqrt{\sqrt{13}-\sqrt{12}}} \) we get:
\( \sqrt{13}+2\sqrt3 \)
\( \sqrt{13}-\sqrt{12} \)
\( 1 \)
\( 25 \)
Expressions with exponents and radicals
1003158602
Level:
C
If \( a=\frac1{\sqrt3-1} \) and \( b=\frac1{\sqrt5-1}-\frac2{\sqrt5}+1 \), then:
\( a > b \)
\( a < b \)
\( a = b \)
\( a = -b \)
1003158601
Level:
C
The number \( \sqrt[5]9 \) is bigger than:
\( 3^{0.3} \)
\( \sqrt3 \)
\( \sqrt[9]{81} \)
\( 3 \)
1003118205
Level:
C
The approximate value of the number \( 10^{0.1} \) to five decimal places is \( 1.25893 \). Give the approximate value of the number \( 10^{-0.9} \) to three decimal places. Do not use a calculator.
\( 0.126 \)
\( 1.259 \)
\( 12.589 \)
\( 7.943 \)
1003118204
Level:
C
The approximate value of the number \( 1.3\cdot10^{-0.4} \) is \( 0.5175393 \). What is the approximate value of the number \( 39\cdot10^{0.6} \)? Give your answer to three decimal places. Do not use a calculator.
\( 155.262 \)
\( 1552.618 \)
\( 15.526 \)
\( 1552.617 \)
1003118203
Level:
C
Assuming \( 12 < \sqrt{153} < 13 \), 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:
C
The 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:
C
Suppose 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:
C
Let \( \frac{u\sqrt5}{5-\sqrt5}=\frac{\frac{5+\sqrt5}{\sqrt5+1}}{1-\sqrt5} \). What is the reciprocal of \( u \)?
\( \frac1u=-\frac{\sqrt5}5 \)
\( \frac1u = \frac1{\sqrt5} \)
\( \frac1u = \frac5{\sqrt5} \)
\( \frac1u = -\sqrt5 \)
1003118109
Level:
C
Which of the following numbers has the same unit digit as the number \( 555^{555} \)?
\( 10^{555}+5 \)
\( \frac{10^{555}}5 \)
\( 5\cdot10^{555} \)
\( 10^{555}+10^{555} \)