2010004801
Level:
A
The value of the expression \( \sqrt[3]{81}-\sqrt{48}+5\sqrt{27}-\sqrt[3]{375} \) is equal to:
\( -2\sqrt[3]3+11\sqrt3 \)
\( 2\sqrt[3]9+11\sqrt3 - 5\sqrt[3]{15}\)
\(- 2\sqrt[3]3-\sqrt{3} \)
\( 2\sqrt[3]9-\sqrt3-5\sqrt[3]{15} \)
Expressions with powers and roots
2010004805
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x\cdot \root{3}\of{x^{7}}
\]
\(x^{3}\root{3}\of{x}\)
\(x^{7}\root{3}\of{x}\)
\(x^{8}\root{3}\of{x}\)
\(x^2\root{3}\of{x^2}\)
2010005601
Level:
A
The mean distance of Uranus from the Sun is \( 4.53\cdot10^{12}\,\mathrm{m} \), and the mean distance of Mercury from the Sun is \( 5.79\cdot10^{10}\,\mathrm{m} \). How many times farther Uranus from the Sun than Mercury is?
about \( 78 \) times
about \( 780 \) times
\( 130\) times
about \( 8\) times
2010005602
Level:
A
Rationalize the denominator of \( \frac{\sqrt{3}-3}{\sqrt 3} \).
\(1- \sqrt 3 \)
\( -3 \)
\( 1+\sqrt3 \)
\( 1-\sqrt3\)
2010005603
Level:
A
Rationalize the denominator of \( \frac1{\sqrt[3]5} \).
\( \frac{\sqrt[3]{25}}{5} \)
\( \frac15 \)
\( \frac{\sqrt[3]{5}}{5} \)
\( \frac{\sqrt5}5 \)
2010005604
Level:
A
Simplifying \( \frac23\sqrt{27} + \sqrt{81} - \sqrt{12} + \frac14\sqrt{48} \) you get:
\( 9+\sqrt3 \)
\( 3+3\sqrt{3} \)
\( 9+5\sqrt{3} \)
\( 15-\sqrt{3} \)
2010005605
Level:
A
Calculate \( \left(2\sqrt{72}-3\sqrt{50}+2\sqrt{32}\right)^2 \).
\( 50 \)
\( 100 \)
\( 5 \)
\( 25 \)
2010005606
Level:
A
The sum of \( 4^{50}+4^{50}+4^{50}+4^{50} \) equals:
\( 4^{51} \)
\( 4^{54} \)
\( 4^{200} \)
\( 16^{50} \)
9000010501
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x^{5}}
\]
\(x\root{3}\of{x^{2}}\)
\(x^{2}\root{3}\of{x^{2}}\)
\(x^{3}\root{3}\of{x^{2}}\)
\(x^{2}\root{5}\of{x^{3}}\)
9000010502
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x^{5}}\cdot \root{3}\of{x^{4}}
\]
\(x^{3}\)
\(\root{3}\of{x^{12}}\)
\(\root{3}\of{x}\)
\(x\root{3}\of{x^{4}}\)