Question

Which of the following statements is incorrect?

A. 1<√2<2
B. 5<√37<6
C. 9<√90 <10
D. 14<√210 <15

Answer 1

The incorrect statement among the options given is Option D: 14<√210 <15, because the square of 14 is 196 and the square of 15 is 225, and 210 does not fall between those two values.

Step-by-step explanation:

The student has asked which of the following statements is incorrect:

• A. 1<√2<2
• B. 5<√37<6
• C. 9<√90 <10
• D. 14<√210 <15

To find the incorrect statement, we can evaluate each option by squaring the numbers that bound the square roots:

1. Option A: 1² = 1 and 2² = 4. Since 2 is greater than √2 and 1 is less than √2, this statement is true.
2. Option B: 5² = 25 and 6² = 36. Since 37 is between 25 and 36, √37 is between 5 and 6, so this statement is also true.
3. Option C: 9² = 81 and 10² = 100. Since 90 is between 81 and 100, √90 is between 9 and 10, and this statement is true.
4. Option D: 14² = 196 and 15² = 225. Here, 210 is not between 196 and 225. This means that √210 is not between 14 and 15, so this statement is incorrect.

The incorrect statement is Option D: 14<√210 <15.