Question
Guess the irrational numbers that lies between 
Hint:
Irrational numbers refer to those numbers that cannot be represented as a simple fraction.
The correct answer is:
GIVEN-
Given numbers- 3√2 and 2√3
TO FIND-
Irrational numbers between the given numbers from the given options
SOLUTION-
We know that-
3√2 = √(3*3) * √2 = √9 * √2 = √18 ...................................... (m = √m * √m)
2√3 = √(2*2) * √3 = √4 * √3 = √12 ...................................... (m = √m * √m)
Hence, we need to find irrational numbers that are between √12 and √18.
We know that whole numbers between 12 & 18 are 13, 14, 15, 16 and 17.
Hence, the irrational numbers between √12 and √18 are √13, √14, √15 and √17 (because √16 = 4, which is not an irrational number)
From the given options, option a satisfies this condition.
FINAL ANSWER-
Option 'a' i.e. '√13 and √14' is the correct answer to the given question.
Related Questions to study
If the digit in one’s place of a number is 3, then the last digit of its cube will be
If the digit in one’s place of a number is 3, then the last digit of its cube will be
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The square root of
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How many two-digit numbers satisfy the following property given below:
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Two-third of two-fifth of three-fourth of a number is 36. What is the square root of four-fifth of that number?
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The cube root of .000216 is
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What is the smallest number by which 3600 be divided to make it a perfect cube?
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The largest four-digit number, which is a perfect cube, is:
The largest four-digit number, which is a perfect cube, is:
The least number that should be multiplied with 1008 to make it a perfect square is
Alternatively, the question can be solved by multiply numbers in each of the options given and then check whether the resultant number is a perfect square or not-
a. 5
1008 * 5 = 5040
We know that 5040 is not a perfect square because √5040 = 12√35.
b. 2
1008 * 2 = 2016
We know that 2016 is not a perfect square because √2016 = 12√14.
c. 7
1008 * 7 = 7056
We know that 7056 is a perfect square because √7056 = 84.
d. 8
1008 * 8 = 8064
We know that 8064 is not a perfect square because √8064 = 24√14.
FINAL ANSWER REMAINS THE SAME.
The least number that should be multiplied with 1008 to make it a perfect square is
Alternatively, the question can be solved by multiply numbers in each of the options given and then check whether the resultant number is a perfect square or not-
a. 5
1008 * 5 = 5040
We know that 5040 is not a perfect square because √5040 = 12√35.
b. 2
1008 * 2 = 2016
We know that 2016 is not a perfect square because √2016 = 12√14.
c. 7
1008 * 7 = 7056
We know that 7056 is a perfect square because √7056 = 84.
d. 8
1008 * 8 = 8064
We know that 8064 is not a perfect square because √8064 = 24√14.
FINAL ANSWER REMAINS THE SAME.
