1003118005
Level:
B
Determine the numbers \( a \) and \( b \) if you know that \( \left(\sqrt5-3\right)\left(a\sqrt5+b\right)=-9\sqrt5+5\sqrt5 \).
\( a=3\text{, }b=5 \)
\( a=\sqrt5\text{, }b=3 \)
\( a=-3\text{, }b=1 \)
\( a=5\text{, }b=\sqrt5 \)
Expressions with powers and roots
1003118009
Level:
B
The square of the number \( \sqrt2-\sqrt[4]2 \) is equal to:
\( 2-2\sqrt[4]8+\sqrt2 \)
\( 2-2\sqrt[4]2+\sqrt2 \)
\( 2-2\sqrt[16]8+\sqrt[8]2 \)
\( 2-\sqrt2 \)
1003118103
Level:
B
Express \( \frac{\sqrt[3]5\sqrt[6]5}{3\cdot25^3+2\cdot125^2} \) as a power of \( 5 \).
\( 5^{-\frac{13}2} \)
\( 5^{-5} \)
\( 5^{-6} \)
\( 5^{-\frac{11}2} \)
1003118107
Level:
B
The number \( \left(\frac{27^{-4}\cdot8^{-4}}{16^{-2}\cdot9^{-5}}\right)^{-3} \) equals:
\( 12^{6} \)
\( 6^6 \)
\( 6^{12} \)
\( \frac1{3^6\cdot2^{12}} \)
1003118603
Level:
B
Select the number that equals \( \sqrt[5]{64} \).
\( 2\sqrt[5]2 \)
\( \frac{\sqrt[5]2}2 \)
\( \sqrt2 \)
\( 2 \)
1003118605
Level:
B
If \( \frac{2\cdot\sqrt[3]2}{\sqrt8} = 2^x \), then
\( x=-\frac16 \).
\( x=0 \).
\( x=\frac13 \).
\( x=-4 \).
1003118607
Level:
B
Which of the following numbers are ordered from least to greatest?
\( (0.3)^4 \), \( 0.027 \), \( (0.3)^{\sqrt2} \)
\( 81^{\frac34} \), \( 16^{\frac14} \), \( 7^{-2} \)
\( \left(\frac23 \right)^{1.4} \), \( \left(\frac23 \right)^{\pi} \), \( \left(\frac32 \right)^{-1} \)
\( 7^0 \), \( 7^{-1} \), \( 7^{-2} \)
1003118608
Level:
B
Express the value of the expression \( \left(\frac23-2^{-2}\right)^{-1} \) as a decimal number.
\( 2.4 \)
\( 0.41\overline6\dots\)
\( \frac{12}5 \)
\( -1.\overline3 \)
1003124901
Level:
B
The fraction \( \frac{1+\sqrt3}{3+\sqrt{11}} \) is equal to:
\( \frac{\sqrt{11}-3}{\sqrt3-1}\)
\( 9 \)
\( \frac{\sqrt{11}-3}{1-\sqrt3} \)
\( \frac{\sqrt{11}+2\sqrt3}2 \)
1003124907
Level:
B
The multiplicative inverse of the number \( \frac{\sqrt[3]{27^2}:9^{\frac12}}{\sqrt[3]9} \) is:
\( 3^{-\frac13} \)
\( 3^{\frac23} \)
\( 3^{\frac13} \)
\( 3^{-\frac23} \)