1003158601
Level:
C
The number \( \sqrt[5]9 \) is bigger than:
\( 3^{0.3} \)
\( \sqrt3 \)
\( \sqrt[9]{81} \)
\( 3 \)
Expressions with exponents and radicals
1003158602
Level:
C
If \( a=\frac1{\sqrt3-1} \) and \( b=\frac1{\sqrt5-1}-\frac2{\sqrt5}+1 \), then:
\( a > b \)
\( a < b \)
\( a = b \)
\( a = -b \)
1003158603
Level:
C
After rationalizing the denominator \( \frac{\sqrt{\sqrt{13}+\sqrt{12}}}{\sqrt{\sqrt{13}-\sqrt{12}}} \) we get:
\( \sqrt{13}+2\sqrt3 \)
\( \sqrt{13}-\sqrt{12} \)
\( 1 \)
\( 25 \)
1003158604
Level:
C
After rationalizing the denominator \( \frac4{1-\sqrt2+\sqrt3} \) we get:
\( \sqrt6-\sqrt2+2 \)
\( -4 \)
\( \sqrt6-\sqrt2 \)
\( 1+\sqrt2-\sqrt3 \)
1003158605
Level:
C
Using the formula for factoring \( a^3-b^3 \) to rationalize the denominator of \( \frac2{\sqrt[3]{25}+\sqrt[3]{15}+\sqrt[3]{9}} \) you get:
\( \sqrt[3]5-\sqrt[3]3 \)
\( 2 \)
\( 2\sqrt[3]{49} \)
\( 2\left( \sqrt[3]{25}-\sqrt[3]{15-\sqrt[3]9}\right) \)
1003158606
Level:
C
Using the formula for factoring \( a^3-b^3 \) to find the multiplicative inverse of \( x=\sqrt[3]3-\sqrt[3]4 \) you get:
\( -\sqrt[3]9-\sqrt[3]{12}-\sqrt[3]{16} \)
\( \sqrt[3]9-\sqrt[3]{12}+\sqrt[3]{16} \)
\( \sqrt[3]3-\sqrt[3]4 \)
\( \sqrt[3]4-\sqrt[3]3 \)
1003158607
Level:
C
As a result of this mathematical action \( \sqrt[3]{\left[\left(\sqrt2+1\right)^3-\left(\sqrt2-1\right)^3\right]^2-13^2} \) we get:
\( 3 \)
\( \sqrt[3]{-170} \)
\( \sqrt[3]{13} \)
\( \sqrt[3]{-168} \)
1003158608
Level:
C
As a result of this mathematical action \( \frac1{\sqrt2+1}+\frac1{\sqrt3+\sqrt2}+\frac1{\sqrt4+\sqrt3}+\dots+\frac1{\sqrt{100}+\sqrt{99}} \) we get:
\( 9 \)
\( 12 \)
\( 100 \)
\( 99 \)
1003158609
Level:
C
Choose the correct relation.
\( \frac{4^{2\sqrt3}\cdot8}{16^{\sqrt3+1}} =\frac12 \)
\( \frac{9^{2\sqrt5}\cdot27^{\frac13}}{81^{1-\sqrt5}} =\frac1{27} \)
\( \frac{\pi^{1-\sqrt2}\cdot\pi^{1+\sqrt2}}{\pi^2} < \frac1{\pi^3} \)
\( \frac{2^{2\pi}\cdot9^{\pi}}{36^{\pi-1}} < 6 \)
1003164001
Level:
C
After simplifying the expression
\[ \sqrt[3]{5\sqrt2+7}-\sqrt[3]{5\sqrt2-7} \]
we get:
\( 2 \)
\( 2\sqrt[3]{57} \)
\( 1 \)
\( 2\sqrt[3]{97} \)