1003099607
Level:
A
Let \( \frac{m}{6-\sqrt6}=\frac{6+\sqrt6}6 \), determine \( m \).
\( m=5 \)
\( m=6 \)
\( m=1 \)
\( m=-5 \)
Expressions with exponents and radicals
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:
\( 1 \)
\( 3\sqrt[6]3 \)
\( 3\sqrt[3]3 \)
\( 3 \)
1003099604
Level:
A
Express \( \left(\sqrt2+3\right)^2 \) in the simplest form:
\( 11+6\sqrt2 \)
\( 11 \)
\( 6\sqrt2 \)
\( 5 \)
1003099603
Level:
A
Calculate \( \left(2\sqrt{75}-3\sqrt{48}+2\sqrt{27}\right)^2 \).
\( 48 \)
\( 192 \)
\( 12 \)
\( 60 \)
1003099602
Level:
A
Simplifying \( \frac32\sqrt8 + \sqrt{16} + \sqrt{32} - \frac13\sqrt{18} \) you get:
\( 4+6\sqrt2 \)
\( 4+\sqrt{12} \)
\( 2+\sqrt{56} \)
\( 4+\sqrt{40} \)
1003099601
Level:
A
Given the numbers \( x=1+2\sqrt2 \) and \( y=\sqrt2-1 \), calculate \( xy \).
\( 3-\sqrt2 \)
\( 4-\sqrt2 \)
\( 3 \)
\( -\sqrt2 \)
1003118010
Level:
C
The product of the number \( \sqrt{\sqrt2+1} \) and the multiplicative inverse of \( \sqrt{\sqrt2-1} \) is equal to:
\( 1+\sqrt2 \)
\( 2\sqrt2 \)
\( 1-\sqrt2 \)
\( 1 \)
1003118009
Level:
B
The square of the number \( \sqrt2-\sqrt[4]2 \) is equal to:
\( 2-2\sqrt[4]8+\sqrt2 \)
\( 2-2\sqrt[4]2+\sqrt2 \)
\( 2-2\sqrt[16]8+\sqrt[8]2 \)
\( 2-\sqrt2 \)
1003118008
Level:
C
Let \( a=\frac1{5+\sqrt3}+\frac1{44-22\sqrt3} \). Choose the correct statement about the number \( a \).
It is a rational number.
It is a positive integer.
It is an irrational number.
It is greater than \( 1 \).