1003134507
Level:
B
In the expansion of \( \left( 2\sqrt3x+4y\right)^3 \) the coefficient of \( xy^2 \) is:
\( 96\sqrt3 \)
\( 32\sqrt3 \)
\( 48 \)
\( 144 \)
Expressions with Exponents and Radicals
1003134506
Level:
B
The number \( \left( \sqrt{2-\sqrt3}-\sqrt{2+\sqrt3} \right)^2 \) equals:
\( 2 \)
\( 4 \)
\( \sqrt3 \)
\( 2\sqrt3 \)
1003134504
Level:
B
The equality \( \left( \sqrt2-a\right)^3 = 2\sqrt2+18+3\sqrt2a^2-a^3 \) is valid for:
\( a=-3 \)
\( a=9 \)
\( a=3 \)
\( a=-9 \)
1003134503
Level:
B
The cube of the number \( 4+3\sqrt2 \) equals:
\( 280+198\sqrt2 \)
\( 64+27\sqrt2 \)
\( 280 + 171\sqrt2 \)
\( 64+52\sqrt2 \)
1003134502
Level:
B
The last digit of the number \( 7^{2015} \) is:
\( 3 \)
\( 7 \)
\( 9 \)
\( 1 \)
1003134501
Level:
B
The number \( 4^{100}\cdot\left(\frac12\right)^{-500}\cdot\sqrt[3]{8^{-300}} \) is equal to the number \( 2^p \). It means that:
\( p=400 \)
\( p=300 \)
\( p=800 \)
\( p = 700 \)
1003124910
Level:
A
The value of the expression \( \sqrt[3]{16}-\sqrt{50}+5\sqrt{32}-\sqrt[3]{250} \) is equal to:
\( -3\sqrt[3]2+15\sqrt2 \)
\( -3\sqrt[3]2+6\sqrt2 \)
\( 2\sqrt[3]4-26\sqrt2-5\sqrt[3]{10} \)
\( 2\sqrt[3]4+6\sqrt2-5\sqrt[3]{10} \)
1003124909
Level:
B
The number \( \frac1{2^{2015}}\cdot(0.0005)^{2015} \) equals:
\( (0.00025)^{2015} \)
\( \frac1{2000^{2015}} \)
\( (0.001)^{2015} \)
\( (0.0025)^{2015} \)
1003124908
Level:
B
Half the inverse of the cube of the number \( 8^{19} \) is:
\( 4^{-86} \)
\( 2^{170} \)
\( \frac1{8^{57}} \)
\( \frac1{2^{170}} \)
1003124907
Level:
B
The multiplicative inverse of the number \( \frac{\sqrt[3]{27^2}:9^{\frac12}}{\sqrt[3]9} \) is:
\( 3^{-\frac13} \)
\( 3^{\frac23} \)
\( 3^{\frac13} \)
\( 3^{-\frac23} \)