Is the lower number 2 ? If it is, then 2² is less than 3. 2² is 4. That's more than 3. So 2 is too big to be the lower number. 2 can be the upper number.
Is the lower number 1 ? If it is, then 1² is less than 3. 1² is 1. 1 is less than 3. So 1 can be the lower number.
√3 is between the two rational numbers 2 and 3. ____________________________________
Numbers with 1 decimal place:
Can the lower number be 1.9 ? If it can, then 1.9² is less than 3. 1.9² is 3.61. That's more than 3. So 1.9 is too big to be the lower number.
Can the lower number be 1.8 ? If it can, then 1.8² is less than 3. 1.8² is 3.24. That's more than 3. So 1.8 is too big to be the lower number.
Can the lower number be 1.7 ? If it can, then 1.7² is less than 3. 1.7² is 2.89. Yay ! That's less than 3. So 1.7 can be the lower number.
√3 is between the rational numbers 1.7 and 1.8 . ____________________________
Numbers with 3 decimal places:
Can the lower number be 1.741 ? If it can, then 1.741² is less than 3. 1.741² is 3.031... . That's more than 3. So 1.741 is too big to be the lower number.
Can the lower number be 1.735 ? If it can, then 1.735² is less than 3. 1.735² is 3.0102... . That's more than 3. So 1.735 is too big to be the lower number.
Can the lower number be 1.734 ? If it can, then 1.734² is less than 3. 1.734² is 3.0067... . That's more than 3. So 1.734 is too big to be the lower number.
Can the lower number be 1.733 ? If it can, then 1.733² is less than 3. 1.733² is 3.00328... . That's more than 3. So 1.733 is too big to be the lower number.
Can the lower number be 1.732 ? If it can, then 1.732² is less than 3. 1.732² is 2.9998... . Yay! That's less than 3.
√3 is between the rational numbers 1.732 and 1.733 . ____________________________________
Of course, if you already KNOW the square root of 3, or if you go to a book or a calculator and find out what it is, or if you know how to figure out what it is and you take a pencil and paper and you do that, then you can just pick any old rational number that's bigger and any old rational number that's smaller, and say "THERE ! Here are two rational numbers that √3 is between."
On my calculator, √3 starts out with
1.7320508 ... So it must be between the two rational numbers 1.7320507 and 1.7320509 . ____________________________
In the question you posted, they GAVE you some pairs of rational numbers. You can test each pair and see if it works. If the √3 is between them, then (the smaller one)² must be less than 3, and (the bigger one)² must be more than 3.
Let's checkum out:
A). 1.2 and 1.3 (1.2)² = 1.44 . Could be ! Let's check the other one. (1.3)² = 1.69 . Aw shucks. The √3 is bigger than both of them, not between them.
B). 1.7 and 1.8 (1.7)² = 2.89 . Could be! Let's check the other one. (1.8)² = 3.24. Yay ! The √3 is between these.
C). 2.6 and 2.7 (2.6)² = 6.76. Phooey! The √3 can't be 'between' these, because it's even smaller than the smaller number.
D). 2.7 and 2.8 (2.7)² = 7.29. Phooey! The √3 can't be 'between' these, because it's even smaller than the smaller number.
Let's first break it down to the time 8 people need for one wall. That would be 10 minutes, right? If one person would have to do it in stead of 8, you'd expect him to take 80 minutes.
To paint 7 walls, he would nee 7x80 = 560 minutes. 10 people would do that 10 times faster, ie., 56 minutes.
I know puzzles like these always have a mindtrick. Did I miss anything?? ;-)
The square root function has no horizontal shift, so the expression under the radical is simply x with no added terms. There is only one such answer choice, which also shows the necessary translation downward by an added negative constant.
As per consensus of India 2011, the population of India is 1,210,193,422. According to the numbers, Uttar Pradesh is the most populous state and Sikkim is the least populous state in Indi
