1003164002
Level:
C
After simplifying the expression
\[ a=\sqrt{6-2\sqrt5}-\sqrt5 \]
we get:
\( -1 \)
\( 6-\sqrt5 \)
\( 6+\sqrt5 \)
\( 1-2\sqrt5 \)
Expressions with powers and roots
1003164003
Level:
C
Let
\[ a=\left[\left(2-\sqrt3\right)^{\frac12}+\left(2+\sqrt3\right)^{\frac12}\right]^2,\ b=\frac{81^{-1}\cdot\sqrt3}{27^{-2}\cdot\sqrt[4]9}.\]
Comparing the numbers \( a^b \) and \( b^a \) you get:
\( a^b > b^a \)
\( a^b < b^a \)
\( a^b \leq b^a \)
\( a^b = b^a \)
1003164004
Level:
C
Evaluate the expression
\[ \frac{5x^2+10x+10}{(x+1)^4-1}\]
for \( x=\sqrt5-2 \) and write the result in the form \( a+b\sqrt c \), where \( a \), \( b \), \( c \) are natural numbers.
\( 5+2\sqrt5 \)
\( 2+5\sqrt2 \)
\( 5+5\sqrt2 \)
\( 5+5\sqrt5 \)
1003164005
Level:
C
Evaluate the expression
\[ \sqrt[3]{\sqrt[3]{10}-\sqrt[3]2}\cdot\sqrt[3]{\sqrt[3]{100}+\sqrt[3]{20}+\sqrt[3]4}. \]
\( 2 \)
\( 8 \)
\( \sqrt[3]{10}-\sqrt[3]2 \)
\( \sqrt[3]{100}-\sqrt[3]4 \)
2010004809
Level:
C
Evaluate the following expression at \(x = 9\).
\[
\frac{x^{-2}}
{x^{-\frac{1}{2}} - x^{-1}}
\]
\(\frac{1}
{18}\)
\(-\frac{1}
{18} \)
\(\frac{27}
{2}\)
\(-\frac{27}
{8}\)
9000079209
Level:
C
Evaluate the following expression at \(x = 4\).
\[
\frac{x^{-\frac{1}
{2} }}
{x^{-2} - x^{-1}}
\]
\(-\frac{8}
{3}\)
\(\frac{31}
{3} \)
\(\frac{8}
{3}\)
\(6\)
9000085602
Level:
C
Evaluate the following numbers and round to the nearest tens.
\[
\left [(2^{2})^{2}\right ]^{2}
\]
\(260\)
\(510\)
\(120\)
\(60\)