Between which two consecutive integers does the square root of 210 lie?
How to approach this question
Think about the square numbers you know. Calculate the squares of integers (10x10, 11x11, 12x12, etc.) until you find two consecutive squares where 210 is between them. The square roots of these two square numbers will be the two consecutive integers you are looking for.
Full Answer
We need to find two consecutive square numbers that 210 lies between.
10² = 100
11² = 121
12² = 144
13² = 169
14² = 196
15² = 225
210 is between 196 and 225.
So, √210 is between √196 and √225.
Therefore, √210 is between 14 and 15.
To find which two consecutive integers the square root of 210 lies between, we need to find two consecutive perfect squares that 210 lies between.
Let's test some integers:
- 10² = 100 (too small)
- 12² = 144 (too small)
- 14² = 196
- 15² = 225
Since 196 < 210 < 225, we can take the square root of the entire inequality:
√196 < √210 < √225
This means:
14 < √210 < 15
So, the square root of 210 lies between the consecutive integers 14 and 15.
Common mistakes
✗ Stating the square numbers (196 and 225) instead of the integers (14 and 15).
✗ Calculation errors when squaring numbers.
✗ Choosing two integers that are not consecutive.
Expert