9000013507
Level:
B
Simplify \(\root{4}\of{16\cdot 81}\).
\(6\)
\(36\)
\(\sqrt{6}\)
\(\root{4}\of{6}\)
Expressions with powers and roots
9000079207
Level:
B
Assuming \(x\not \in \{0;1;3\}\),
simplify the following expression.
\[
\frac{x^{2} - 9}
{x^{2} - x}\cdot \left (\frac{x^{2} - 3x}
{x - 1} \right )^{-1}
\]
\(\frac{x+3}
{x^{2}} \)
\(\frac{x-3}
{x^{2}} \)
\(\frac{x+3}
{2x} \)
\(\frac{x+3}
{x} \)
1003034108
Level:
C
Give the result of the gradual exponentiation \(\left(\left(\left(\left(2\right)^2\right)^0\right)^3\right)^4\):
\( 1 \)
\( 0 \)
\( 4^{12} \)
\( 2^9 \)
1003109205
Level:
C
The bank offers a term deposit with annual interest rate of \( 0.9\% \). We need to tax our profits with the income tax of \( 15\% \). How many Euros are we going to have after five years of savings if the original deposit is \( 200 \) Euros?
\( 207.77 \)
\( 209.36 \)
\( 371.8 \)
\( 209.16 \)
\( 207.65 \)
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:
\( 9 \)
\( 3 \)
\( \sqrt3 \)
\( \sqrt[3]3 \)
1003118002
Level:
C
The number \( \sqrt{7-4\sqrt3} + \sqrt{7+4\sqrt3} \) is equal to:
\( 4 \)
\( \sqrt{14} \)
\( 16 \)
\( 8\sqrt3 \)
1003118003
Level:
C
Give the multiplicative inverse of \( \frac{\sqrt[3]4-\sqrt[3]2}2 \).
\( 2\sqrt[3]2 + 2 +\sqrt[3]4 \)
\( \sqrt[3]{12}+2+\sqrt[3]4 \)
\( 2\sqrt[3]{12}+2+\sqrt[3]4 \)
\( \sqrt[3]{2}+2+\sqrt[3]4 \)
1003118004
Level:
C
The number \( \sqrt{3-2\sqrt2} \) equals:
\( \sqrt2-1 \)
\( 1-\sqrt2 \)
\( \sqrt2 \)
\( \sqrt3-\sqrt{2\sqrt2} \)
1003118006
Level:
C
Give the value of the expression \( \sqrt{\left(2-\sqrt7\right)^2}-\sqrt{\left(3+\sqrt7\right)^2} \).
\( -5 \)
\( -1 \)
\( -1-2\sqrt7 \)
\( -5+2\sqrt7 \)
1003118007
Level:
C
Calculate the fourth power of the number \( 1-\sqrt2 \).
\( 17-12\sqrt2 \)
\( 17-4\sqrt2 \)
\( 3-2\sqrt2 \)
\( 9-4\sqrt2 \)