1003099503 Level: BLet \( a = 2\sqrt7 + \sqrt5 \) and \( b=\frac1{\sqrt7-\sqrt5} \). Choose the right relation between \( a \) and \( b \).\( a > b \)\( a = b \)\( a < b \)\( a + b = 0 \)
1003099502 Level: BSimplify 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: BLet \( x=4^{-1}+4^{-\frac12}-\left(\frac{\sqrt2}2\right)^2 \). Which of the following inequalities is true?\( x \geq 2^{-2} \)\( x < 4^{-1} \)\( x > 2 \)\( x \leq 4^{-3} \)
1003099609 Level: BComplete 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: BChoose 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.
1003099607 Level: ALet \( \frac{m}{6-\sqrt6}=\frac{6+\sqrt6}6 \), determine \( m \).\( m=5 \)\( m=6 \)\( m=1 \)\( m=-5 \)
1003099606 Level: BCalculate 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: BSimplifying \( \left( \sqrt[3]{3\sqrt9} \right)^{\frac32} \sqrt{9^{-1}} \) we get:\( 1 \)\( 3\sqrt[6]3 \)\( 3\sqrt[3]3 \)\( 3 \)
1003099604 Level: AExpress \( \left(\sqrt2+3\right)^2 \) in the simplest form:\( 11+6\sqrt2 \)\( 11 \)\( 6\sqrt2 \)\( 5 \)
1003099603 Level: ACalculate \( \left(2\sqrt{75}-3\sqrt{48}+2\sqrt{27}\right)^2 \).\( 48 \)\( 192 \)\( 12 \)\( 60 \)