insert a rational number between following:
0.25 and 0.26
3.413and 4.314
4.13692 and 4.4568
sqrt3 and sqrt5
To insert a rational number between two given numbers, we need to find a number that lies between them and can be expressed as a fraction. Here's how you can find rational numbers between the given numbers:
1. Between 0.25 and 0.26:
The simplest way to find a rational number is to take the average of the two numbers. In this case:
Average = (0.25 + 0.26) / 2 = 0.255
So, the rational number between 0.25 and 0.26 is 0.255.
2. Between 3.413 and 4.314:
Similar to the previous case, we find the average:
Average = (3.413 + 4.314) / 2 = 3.8635
So, a rational number between 3.413 and 4.314 is 3.8635.
3. Between 4.13692 and 4.4568:
Again, find the average:
Average = (4.13692 + 4.4568) / 2 = 4.29686
So, a rational number between 4.13692 and 4.4568 is 4.29686.
4. Between √3 and √5:
In this case, both numbers are irrational (square roots). To find a rational number between them, we can use decimal approximations. Let's round the square roots to two decimal places:
√3 ≈ 1.73
√5 ≈ 2.24
Similar to the previous cases, find the average:
Average = (1.73 + 2.24) / 2 = 1.985
So, a rational number between √3 and √5 is approximately 1.985.
Remember that these approximations are rational numbers and may not be exact fractions.
a simple way is to find the average of the two numbers
for the last one, wouldn't √4 lie between √3 and √5 ?
and √4 = 2, so there you have it