1003118007
Level:
C
Calculate the fourth power of the number \( 1-\sqrt2 \).
\( 17-12\sqrt2 \)
\( 17-4\sqrt2 \)
\( 3-2\sqrt2 \)
\( 9-4\sqrt2 \)
Expressions with exponents and radicals
1003118006
Level:
C
Give the value of the expression \( \sqrt{\left(2-\sqrt7\right)^2}-\sqrt{\left(3+\sqrt7\right)^2} \).
\( -5 \)
\( -1 \)
\( -1-2\sqrt7 \)
\( -5+2\sqrt7 \)
1003118005
Level:
B
Determine the numbers \( a \) and \( b \) if you know that \( \left(\sqrt5-3\right)\left(a\sqrt5+b\right)=-9\sqrt5+5\sqrt5 \).
\( a=3\text{, }b=5 \)
\( a=\sqrt5\text{, }b=3 \)
\( a=-3\text{, }b=1 \)
\( a=5\text{, }b=\sqrt5 \)
1003118004
Level:
C
The number \( \sqrt{3-2\sqrt2} \) equals:
\( \sqrt2-1 \)
\( 1-\sqrt2 \)
\( \sqrt2 \)
\( \sqrt3-\sqrt{2\sqrt2} \)
1003118003
Level:
C
Give the multiplicative inverse of \( \frac{\sqrt[3]4-\sqrt[3]2}2 \).
\( 2\sqrt[3]2 + 2 +\sqrt[3]4 \)
\( \sqrt[3]{12}+2+\sqrt[3]4 \)
\( 2\sqrt[3]{12}+2+\sqrt[3]4 \)
\( \sqrt[3]{2}+2+\sqrt[3]4 \)
1003118002
Level:
C
The number \( \sqrt{7-4\sqrt3} + \sqrt{7+4\sqrt3} \) is equal to:
\( 4 \)
\( \sqrt{14} \)
\( 16 \)
\( 8\sqrt3 \)
1003118001
Level:
C
The number \( 3\sqrt[3]3\cdot\sqrt[4]{3\sqrt[3]3}\cdot\sqrt[5]{3\sqrt[3]3\cdot\sqrt[4]{3\sqrt[3]3}} \) is equal to:
\( 9 \)
\( 3 \)
\( \sqrt3 \)
\( \sqrt[3]3 \)
1003032110
Level:
A
Calculate \( \sqrt[3]{-\frac8{125}}-\sqrt[3]{-2\frac{10}{27}} \).
\( \frac{14}{15} \)
\( -\frac25 \)
\( 1\frac2{97} \)
\( 2\frac{18}{152} \)
1003032109
Level:
B
Calculate \( \left(3.4\cdot10^7\right)\cdot\left(4\cdot10^{-5}\right) \) and give the result in the scientific notation.
\( 1\,360 = 1.36\cdot10^3\)
\(1\,360 = 13.6\cdot10^2 \)
\( 1\,360 = 136\cdot10^1\)
\( 1\,360\,000\,000\,000 = 1.36\cdot10^{12}\)
1003032108
Level:
B
Write the number \( 4^{-5}\cdot8^2 \) as \( 2^m \), where \( m \) is an integer.
\( 2^{-4} \)
\( 2^{-3} \)
\( 2^{-16} \)
\( 2^{-30} \)