Question

Grogg typed the following $1000$ expressions into his calculator, one by one: \[\sqrt{1}, \sqrt{2}, \sqrt{3}, \sqrt{4}, \dots, \sqrt{999}, \sqrt{1000}. \]how many times will grogg's result be an integer?

Answer 1

Since 30² = 900 and 40² = 1600, between 30 and 40 of the numbers Grogg enters will reduce to integers. Now just find which count is correct. We don't have to look far:

31² = 961

32² = 1024

so there 31 of the outputs of √1, √2, √3, ..., √1000 are integers.

Answer 2

Grogg will result to integers  with  31  outputs from √1, √2, √3, ..., √1000 .

What are integers?

An integer serves as the whole number which can be a positive or negative numbers , such as 6, 9, but it cannot be a fraction.

since, she is starting from √1, √2, √3, up to √1000 , then we know that

31² = 961, then we can find the correct count which is 31. so if she is to input those number into square root one after the other , she will have 31 count.

Therefore, Grogg will result to integers  with  31  outputs from √1, √2, √3, ..., √1000 .

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