2010004702
Level:
B
Simplify the fraction \( \frac{\sqrt[12]8\cdot\sqrt[20]{16}\cdot\sqrt[5]{15}}{\sqrt[5]{30}} \).
\( \sqrt[4]2 \)
\( \frac1{\sqrt[4]2} \)
\( 1 \)
\( 2 \)
Expressions with exponents and radicals
2010004701
Level:
B
The value of the multiplicative inverse of \( \left[ \left( \frac12 \right)^{-1} -5^{-2}\right]^{\frac12} \) is:
\( \frac57 \)
\( \sqrt2-\frac15 \)
\( \frac{25}{49} \)
\( \frac75 \)
Expressions with Powers and Roots I
Submitted by ladislav.foltyn on Sat, 03/02/2019 - 16:35Question:
In each line of the table, mark the relation that is true.
Reciprocals
Submitted by ladislav.foltyn on Sat, 02/23/2019 - 09:35Expressions with Powers and Roots II
Submitted by ladislav.foltyn on Fri, 02/15/2019 - 14:11Question:
The following diagram presents: \( \mathbb{N} \) -- Natural numbers, \( \mathbb{Z} \) -- Integers, \( \mathbb{Q} \) -- Rational numbers, \( \mathbb{R}\setminus \mathbb{Q} \) -- Irrational numbers. In the table, specify the smallest number set to which the given number belongs.
Numbers in Exponential Form
Submitted by ladislav.foltyn on Fri, 02/15/2019 - 12:56Question:
Mark the option that represents a given number in an exponential notation.
Roots of negative numbers
Submitted by ladislav.foltyn on Sat, 02/09/2019 - 20:02Question:
Calculate the following \( n \)th-roots and mark the correct answers.
1003164006
Level:
B
The value of the expression
\[ \frac{x^4-16}{\left(x^2+4\right)\left(x+2\right) }\]
for \( x=2-\sqrt2 \) is equal to:
\( -\sqrt2 \)
\( \sqrt2 \)
\( 2 \)
\( -2 \)
1003164005
Level:
C
Evaluate the expression
\[ \sqrt[3]{\sqrt[3]{10}-\sqrt[3]2}\cdot\sqrt[3]{\sqrt[3]{100}+\sqrt[3]{20}+\sqrt[3]4}. \]
\( 2 \)
\( 8 \)
\( \sqrt[3]{10}-\sqrt[3]2 \)
\( \sqrt[3]{100}-\sqrt[3]4 \)
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.
\( 5+2\sqrt5 \)
\( 2+5\sqrt2 \)
\( 5+5\sqrt2 \)
\( 5+5\sqrt5 \)