Which irrational number is between square root 14 and square root 18 square root 10 √15 square root 13 or square root 19
To determine which irrational number is between the given options of numbers, we can simplify each square root individually and compare them:
1. Square root of 14:
√14 ≈ 3.74
2. Square root of 18:
√18 ≈ 4.24
3. Square root of 10:
√10 ≈ 3.16
4. Square root of 15:
√15 ≈ 3.87
5. Square root of 13:
√13 ≈ 3.61
6. Square root of 19:
√19 ≈ 4.36
From the given options, the number between the square root of 14 and the square root of 18 is the square root of 15 (approximately 3.87).
To determine which irrational number lies between √14 and √19, we can compare their decimal approximations.
Let's start by finding the decimal approximations for these square roots:
√14 ≈ 3.7416573867739413
√19 ≈ 4.358898943540674
Now, let's examine the given options:
√18 ≈ 4.242640687119285
√10 ≈ 3.1622776601683795
√15 ≈ 3.872983346207417
√13 ≈ 3.605551275463989
Comparing all the decimal approximations, we can see that √18, √15, and √19 are the closest to each other. However, √18 and √15 are still closer to √19 than √14.
Therefore, the irrational number lying between √14 and √19 is √18.