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.
\( (-1.6; -1.4 ) \)
\( (-1.8; -1.5 ) \)
\( (1.4; 1.6 ) \)
\( (1.6; 1.8 ) \)
Expressions with powers and roots
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.
\( 155.262 \)
\( 1552.618 \)
\( 15.526 \)
\( 1552.617 \)
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.
\( 0.126 \)
\( 1.259 \)
\( 12.589 \)
\( 7.943 \)
1003124902
Level:
C
Rationalizing the denominator \( \frac1{\left(2-\sqrt3\right)^3} \) you get:
\( 26+15\sqrt3 \)
\( 27+30\sqrt3 \)
\( 14+7\sqrt3 \)
\( 27+24\sqrt3 \)
1003124903
Level:
C
The number \( \left( \sqrt2+1 \right)^4 \) is greater than the number \( \left( \sqrt2-1 \right)^4 \) by:
\( 24\sqrt2 \)
\( 12\sqrt2 \)
\( 2 \)
\( 4\sqrt2 \)
1003124904
Level:
C
The number\( \sqrt[4]{\left( \sqrt3-\sqrt2 \right)^4}+\sqrt[4]{\left( \sqrt2-\sqrt5 \right)^4}+\sqrt[3]{\left( \sqrt3-\sqrt5 \right)^3} \) equals:
\( 2\sqrt3 - 2\sqrt2 \)
\( 2\sqrt5 - 2\sqrt2 \)
\( 2\sqrt3 - 2\sqrt5 \)
\( 2\sqrt5 - 2\sqrt3 \)
1003124905
Level:
C
Numbers \( \left(2^2\right)^{\left(2^2\right)} \), \( \left(2\right)^{\left({2^2}^2\right)} \), \( \left({2^2}^2\right)^2 \), \( \left(2\right)^{\left(2^2\right)^2} \) were written on the board. How many different numbers are represented by these records?
\( 2 \)
\( 3 \)
\( 4 \)
\( 1 \)
1003124906
Level:
C
The number \( \left(\sqrt7+1\right)^4-\left(\sqrt7-1\right)^4 \) equals:
\( 64\sqrt7 \)
\( 32\sqrt7 \)
\( \sqrt7 \)
\( 2 \)
1003134508
Level:
C
The number \( \left(\sqrt2-1\right)^6 \) is equal to:
\( 99-70\sqrt2 \)
\( 5\sqrt2 - 7 \)
\( 49-35\sqrt2 \)
\( 34-24\sqrt2 \)
1003134510
Level:
C
Complete the following sentence to obtain a true statement. The number \( \left( \sqrt3 \right)^{\sqrt2^{\sqrt[3]{64}}} \) is ...
a rational number less than \( 10 \).
an irrational number less than \( 10 \).
an integer greater than \( 10 \).
a rational number greater than \( 10 \).