1003124910
Level:
A
The value of the expression \( \sqrt[3]{16}-\sqrt{50}+5\sqrt{32}-\sqrt[3]{250} \) is equal to:
\( -3\sqrt[3]2+15\sqrt2 \)
\( -3\sqrt[3]2+6\sqrt2 \)
\( 2\sqrt[3]4-26\sqrt2-5\sqrt[3]{10} \)
\( 2\sqrt[3]4+6\sqrt2-5\sqrt[3]{10} \)
Expressions with powers and roots
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:
\( 3^{-\frac13} \)
\( 3^{\frac23} \)
\( 3^{\frac13} \)
\( 3^{-\frac23} \)
1003124906
Level:
C
The number \( \left(\sqrt7+1\right)^4-\left(\sqrt7-1\right)^4 \) equals:
\( 64\sqrt7 \)
\( 32\sqrt7 \)
\( \sqrt7 \)
\( 2 \)
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?
\( 2 \)
\( 3 \)
\( 4 \)
\( 1 \)
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:
\( 2\sqrt3 - 2\sqrt2 \)
\( 2\sqrt5 - 2\sqrt2 \)
\( 2\sqrt3 - 2\sqrt5 \)
\( 2\sqrt5 - 2\sqrt3 \)
1003124903
Level:
C
The number \( \left( \sqrt2+1 \right)^4 \) is greater than the number \( \left( \sqrt2-1 \right)^4 \) by:
\( 24\sqrt2 \)
\( 12\sqrt2 \)
\( 2 \)
\( 4\sqrt2 \)
1003124902
Level:
C
Rationalizing the denominator \( \frac1{\left(2-\sqrt3\right)^3} \) you get:
\( 26+15\sqrt3 \)
\( 27+30\sqrt3 \)
\( 14+7\sqrt3 \)
\( 27+24\sqrt3 \)
1003124901
Level:
B
The fraction \( \frac{1+\sqrt3}{3+\sqrt{11}} \) is equal to:
\( \frac{\sqrt{11}-3}{\sqrt3-1}\)
\( 9 \)
\( \frac{\sqrt{11}-3}{1-\sqrt3} \)
\( \frac{\sqrt{11}+2\sqrt3}2 \)