1003099508
Level:
A
Evaluate the expression \( \frac{2-x}{x-2} \) for \( x=2-\sqrt2 \).
\( -1 \)
\( \sqrt2 - 2 \)
\( 2 - \sqrt2 \)
\( 1 \)
Expressions with exponents and radicals
1003099507
Level:
B
The multiplicative inverse of \( \frac2{\sqrt3-1} \) is:
\( \frac1{\sqrt3+1} \)
\( \frac2{\sqrt3+1} \)
\( \frac{-2}{\sqrt3-1} \)
\( \frac{1-\sqrt3}2 \)
1003099506
Level:
B
The additive inverse of \( \frac1{5-2\sqrt5} \) is:
\( \frac{-5-2\sqrt5}5 \)
\( \frac{-1}{2\sqrt5-5} \)
\( \frac{-1}{2\sqrt5+5} \)
\( 5-2\sqrt5 \)
1003099505
Level:
A
Rewrite \( \frac{2-\sqrt3}{2+\sqrt3} \) by rationalizing the denominator.
\( 7-4\sqrt3 \)
\( \left(2-\sqrt3\right)\left(2+\sqrt3\right) \)
\( \frac{7-4\sqrt3}5 \)
\( \frac{7-4\sqrt3}7 \)
1003099504
Level:
A
Rationalizing the denominator \( \frac1{\sqrt5+\sqrt7} \) we get:
\( \frac{\sqrt7-\sqrt5}2 \)
\( \frac{\sqrt5+\sqrt7}2 \)
\( \frac{\sqrt5-\sqrt7}2 \)
\( \frac{-\sqrt7-\sqrt5}2 \)
1003099503
Level:
B
Let \( a = 2\sqrt7 + \sqrt5 \) and \( b=\frac1{\sqrt7-\sqrt5} \). Choose the right relation between \( a \) and \( b \).
\( a > b \)
\( a = b \)
\( a < b \)
\( a + b = 0 \)
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.