Mathematics
Grade-8
Easy
Question
Guess the irrational numbers that lies between 3 and 5?
Hint:
Irrational numbers refer to those numbers that cannot be represented as a simple fraction.
The correct answer is: ![square root of 10 space and space square root of 11](data:image/png;base64,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)
GIVEN-
Given numbers- 3 and 5
TO FIND-
Irrational numbers between the given numbers from the given options
SOLUTION-
We know that-
3 = √(3*3) = √9 ...................................... (m = √m * √m)
5 = √(5*5) = √25 ...................................... (m = √m * √m)
Hence, we need to find irrational numbers that are between √9 and √25.
From the given options, option a satisfies this condition.
FINAL ANSWER-
Option 'a' i.e. '√10 and √11' is the correct answer to the given question.
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MathematicsGrade-8
Mathematics
Guess the irrational numbers that lies between ![4 space and space square root of 21](data:image/png;base64,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)
Guess the irrational numbers that lies between ![4 space and space square root of 21](data:image/png;base64,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)
MathematicsGrade-8
Mathematics
What should come in place of both x in the equation
![fraction numerator x over denominator square root of 128 end fraction equals fraction numerator square root of 162 over denominator x end fraction](data:image/png;base64,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)
What should come in place of both x in the equation
![fraction numerator x over denominator square root of 128 end fraction equals fraction numerator square root of 162 over denominator x end fraction](data:image/png;base64,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)
MathematicsGrade-8
Mathematics
Guess the smallest rational numbers among ![negative 4 over 9 comma space fraction numerator 5 over denominator negative 12 end fraction comma space fraction numerator 7 over denominator negative 18 end fraction space and space fraction numerator 2 over denominator negative 3 end fraction](data:image/png;base64,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)
Guess the smallest rational numbers among ![negative 4 over 9 comma space fraction numerator 5 over denominator negative 12 end fraction comma space fraction numerator 7 over denominator negative 18 end fraction space and space fraction numerator 2 over denominator negative 3 end fraction](data:image/png;base64,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)
MathematicsGrade-8