1003099503
Level:
B
Let \( a = 2\sqrt7 + \sqrt5 \) and \( b=\frac1{\sqrt7-\sqrt5} \). Choose the right relation between \( a \) and \( b \).
\( a > b \)
\( a = b \)
\( a < b \)
\( a + b = 0 \)
B
1003099502
Level:
B
Simplify the fraction \( \frac{\sqrt[8]9\cdot\sqrt[12]{27}\cdot\sqrt[4]{14}}{\sqrt[4]{42}} \).
\( \sqrt[4]3 \)
\( \frac1{\sqrt[4]3} \)
\( 1 \)
\( 3 \)
1003099501
Level:
B
Let \( x=4^{-1}+4^{-\frac12}-\left(\frac{\sqrt2}2\right)^2 \). Which of the following inequalities is true?
\( x \geq 2^{-2} \)
\( x < 4^{-1} \)
\( x > 2 \)
\( x \leq 4^{-3} \)
1003099609
Level:
B
Complete the sentence to get a true statement: The numbers \( -\frac{\sqrt3}6-\frac12 \) and \( \sqrt3-3 \) are ...
multiplicative inverses of each other.
equal.
rational numbers.
additive inverses of each other.
1003099608
Level:
B
Choose the correct statement about the number \( 4\sqrt2-\frac{2\sqrt2+2}{\sqrt2-1} \).
It is a rational number.
It is an irrational number.
It is greater than \( \sqrt2 \).
It is a positive integer.
1003099606
Level:
B
Calculate the value of the expression \( \frac{2a+12}{-a^2} \) for \( a=-2\sqrt3 \).
\( \frac{\sqrt3-3}3 \)
\( 4\sqrt3 -1 \)
\( \frac{-\sqrt3+3}3 \)
\( -4\sqrt3+1 \)
1003099605
Level:
B
Simplifying \( \left( \sqrt[3]{3\sqrt9} \right)^{\frac32} \sqrt{9^{-1}} \) we get:
\( 1 \)
\( 3\sqrt[6]3 \)
\( 3\sqrt[3]3 \)
\( 3 \)
1003118009
Level:
B
The square of the number \( \sqrt2-\sqrt[4]2 \) is equal to:
\( 2-2\sqrt[4]8+\sqrt2 \)
\( 2-2\sqrt[4]2+\sqrt2 \)
\( 2-2\sqrt[16]8+\sqrt[8]2 \)
\( 2-\sqrt2 \)
1003118005
Level:
B
Determine the numbers \( a \) and \( b \) if you know that \( \left(\sqrt5-3\right)\left(a\sqrt5+b\right)=-9\sqrt5+5\sqrt5 \).
\( a=3\text{, }b=5 \)
\( a=\sqrt5\text{, }b=3 \)
\( a=-3\text{, }b=1 \)
\( a=5\text{, }b=\sqrt5 \)
1103123809
Level:
B
Choose the equation of which the solution is graphed in the picture.
\( x^2-4x=0 \)
\( x^2-4=0 \)
\( x^2-2x=0 \)
\( x^2-2=0 \)