Tag: rational and irrational numbers
Questions Related to rational and irrational numbers
Classify the following numbers as rational or irrational : $2-\sqrt{5}$
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Irrational number
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Rational number
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Less Data
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None of the above
$2$ is rational
Decimal representation of an irrational number is always
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Terminating
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Terminating, Repeating
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Non-Terminating, Repeating
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Non-Terminating, Non-Repeating
Decimal representation of an irrational number is always non terminating non repeating.
Are the square roots of all positive integers irrational?
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True
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False
No. Not all square roots of integers are irrational. Examples are $\sqrt{4}=2$, $\sqrt{1}=1$, $\sqrt{9}=3$, etc.
Which among the following is true?
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There is no rational number between two irrational numbers.
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If ${x}^{2}=0.4$,then x is a rational number.
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The only real numbers are rational numbers.
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The reciprocal of an irrational number is irrational.
The decimal expansion of the number $\sqrt{2}$ is
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A finite decimal
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1.4121
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Non-Terminating, Recurring
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Non-Terminating, Non-Recurring
$\sqrt{2} = 1.4142136...$
The decimal expansion of the number $\sqrt{2}$ is Non-terminating non recurring
State True or False.
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True
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False
$\ { (\sqrt { 2 } -2) }^{ 2 }=2+4-4\sqrt { 2 } =6-4\sqrt { 2 } \ \sqrt { 2 } =1.41421356237........\ \ \sqrt { 2 } is\quad an\quad irrational\quad number,\quad since\quad its\quad decimal\quad representaion\quad is\quad non\quad terminating\quad non\quad repeating.\ Multiplication\quad and\quad subtration\quad of\quad rational\quad with\quad irrational\quad is\quad irrational.\ Hence,\quad { (\sqrt { 2 } -2) }^{ 2 }\quad is\quad an\quad irrational\quad number.\ \quad $
State True or False.
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True
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False
$\ { (\sqrt { 2 } +\sqrt { 3 } ) }^{ 2 }=2+3+2\sqrt { 6 } =5+2\sqrt { 6 } \ \sqrt { 6 } =2.44948974278........\ \ \sqrt { 6 } is\quad an\quad irrational\quad number,\quad since\quad its\quad decimal\quad representaion\quad is\quad non\quad terminating\quad non\quad repeating.\ Multiplication\quad ans\quad addition\quad of\quad rational\quad with\quad irrational\quad is\quad irrational.\ Hence,\quad { (\sqrt { 2 } +\sqrt { 3 } ) }^{ 2 }\quad is\quad an\quad irrational\quad number.\ \quad $
State True or False.
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True
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False
$\ \sqrt { 3 } =1.73205080757......\ \sqrt { 3 } is\quad an\quad irrational\quad number,\quad since\quad it's\quad decimal\quad representaion\quad is\quad non\quad terminating\quad non\quad repeating.\ And\quad addition\quad of\quad a\quad rational\quad and\quad irrational\quad number\quad is\quad irrational.\ Hence,\quad 2+\sqrt { 3 } \quad is\quad an\quad irrational\quad number.\ \quad $
State True or False.
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True
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False
$\ \sqrt { 3 } =1.73205080757......\ Also\quad \sqrt { 2 } =1.41421356237........\ \sqrt { 3 } and\quad \sqrt { 2 } are\quad irrational\quad numbers,\quad since\quad their\quad decimal\quad representaion\quad is\quad non\quad terminating\quad non\quad repeating.\ And\quad addition\quad of\quad two\quad irrational\quad numbers\quad is\quad irrational.\ Hence,\quad \sqrt { 2 } +\sqrt { 3 } \quad is\quad an\quad irrational\quad number.\ \quad $
State True or False.
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True
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False
$\ \sqrt { 3 } =1.73205080757......\ Also\quad \sqrt { 5 } =2.2360679775........\ \sqrt { 3 } and\quad \sqrt { 5 } are\quad irrational\quad numbers,\quad since\quad their\quad decimal\quad representaion\quad is\quad non\quad terminating\quad non\quad repeating.\ And\quad addition\quad of\quad two\quad irrational\quad numbers\quad is\quad irrational.\ Hence,\quad \sqrt { 5 } +\sqrt { 3 } \quad is\quad an\quad irrational\quad number.\ \quad $