1003099505 Level: ARewrite \( \frac{2-\sqrt3}{2+\sqrt3} \) by rationalizing the denominator.\( 7-4\sqrt3 \)\( \left(2-\sqrt3\right)\left(2+\sqrt3\right) \)\( \frac{7-4\sqrt3}5 \)\( \frac{7-4\sqrt3}7 \)
1003099508 Level: AEvaluate the expression \( \frac{2-x}{x-2} \) for \( x=2-\sqrt2 \).\( -1 \)\( \sqrt2 - 2 \)\( 2 - \sqrt2 \)\( 1 \)
1003099509 Level: AGiven the numbers \( x = 4+2\sqrt5 \) and \( y=6-2\sqrt5 \), the fraction \( \frac xy \) can be written in the form:\( \frac{11+5\sqrt5}4 \)\( \frac{7\sqrt5-9}4 \)\( \frac{-5\sqrt5}2 \)\( 8\sqrt5 \)
1003099601 Level: AGiven the numbers \( x=1+2\sqrt2 \) and \( y=\sqrt2-1 \), calculate \( xy \).\( 3-\sqrt2 \)\( 4-\sqrt2 \)\( 3 \)\( -\sqrt2 \)
1003099602 Level: ASimplifying \( \frac32\sqrt8 + \sqrt{16} + \sqrt{32} - \frac13\sqrt{18} \) you get:\( 4+6\sqrt2 \)\( 4+\sqrt{12} \)\( 2+\sqrt{56} \)\( 4+\sqrt{40} \)
1003099603 Level: ACalculate \( \left(2\sqrt{75}-3\sqrt{48}+2\sqrt{27}\right)^2 \).\( 48 \)\( 192 \)\( 12 \)\( 60 \)
1003099604 Level: AExpress \( \left(\sqrt2+3\right)^2 \) in the simplest form:\( 11+6\sqrt2 \)\( 11 \)\( 6\sqrt2 \)\( 5 \)
1003099607 Level: ALet \( \frac{m}{6-\sqrt6}=\frac{6+\sqrt6}6 \), determine \( m \).\( m=5 \)\( m=6 \)\( m=1 \)\( m=-5 \)
1003118601 Level: ADecide which of the following equations is false.\( \sqrt5-\sqrt2=\sqrt3 \)\( \sqrt{15}:\sqrt3=\sqrt5 \)\( \sqrt5 \cdot \sqrt2 =\sqrt{10} \)\( \sqrt{\sqrt4}=\sqrt2 \)
1003118602 Level: AChoose the number equal to \( \sqrt{18}-\sqrt8 \).\( \sqrt2 \)\( \sqrt{10} \)\( 10 \)\( 5\sqrt2 \)