What is the least integer whose square root is an irrational number between 5 and 7?
Responses
25
26
6
13
3 answers
The least integer whose square root is an irrational number between 5 and 7 is 26.
can you explain
Sure! To find the least integer whose square root is an irrational number between 5 and 7, we need to find the smallest perfect square greater than 5 and the largest perfect square less than 7.
The perfect squares nearest to 5 are 4 (2^2) and 9 (3^2), and the perfect squares nearest to 7 are 4 (2^2) and 9 (3^2).
Since we are looking for an irrational number between 5 and 7, the square root of this number cannot be an integer or any fraction made from perfect squares, like 2 or 3.
The next perfect square greater than 5 is 6^2 = 36, but its square root is 6, which is not an irrational number.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 26.
The square root of 26 is approximately 5.099, which is an irrational number between 5 and 7.
The perfect squares nearest to 5 are 4 (2^2) and 9 (3^2), and the perfect squares nearest to 7 are 4 (2^2) and 9 (3^2).
Since we are looking for an irrational number between 5 and 7, the square root of this number cannot be an integer or any fraction made from perfect squares, like 2 or 3.
The next perfect square greater than 5 is 6^2 = 36, but its square root is 6, which is not an irrational number.
Therefore, the least integer whose square root is an irrational number between 5 and 7 is 26.
The square root of 26 is approximately 5.099, which is an irrational number between 5 and 7.