Recognize Subsets of the Real Numbers
-$B = \left\{ 11 , \sqrt { 7 } , - 11,0 , \frac { 5 } { 6 } , \sqrt { 4 } , 0 . \overline { 7 } , 0.35 \right\}$ Irrational numbers
A) $\sqrt { 7 }$
B) $\sqrt { 7 } , 0 . \overline { 7 }$
C) $\sqrt { 7 } , \sqrt { 4 } , 0 . \overline { 7 }$
D) $\sqrt { 7 } , \sqrt { 4 } , 0.35$

Question

Quizplus · Accepted Answer

Irrational numbers cannot be expressed as a fraction of two integers and have non-repeating, non-terminating decimal expansions. Among the options, only $\sqrt{7}$ fits this description, as $\sqrt{4}$ is rational (equal to 2), and both $0.\overline{7}$ and $0.35$ can be expressed as fractions ($\frac{7}{9}$ and $\frac{35}{100}$ or $\frac{7}{20}$, respectively).

Recognize Subsets of the Real Numbers - B={11,7,−11,0,56,4,0.7‾,0.35}B = \left\{ 11 , \sqrt { 7 } , - 11,0 , \frac { 5 } { 6 } , \sqrt { 4 } , 0 . \overline { 7 } , 0.35 \right\}B={11,7​,−11,0,65​,4​,0.7,0.35}

Recognize Subsets of the Real Numbers
- $B = \left\{ 11 , \sqrt { 7 } , - 11,0 , \frac { 5 } { 6 } , \sqrt { 4 } , 0 . \overline { 7 } , 0.35 \right\}$