Between what two consecutive integers does the square root of 205 lie? A. 11 & 12 B. 12 & 13 C. 13 & 14 D. 14 & 15 20. Which of the statements is TRUE? A. V is a natural number C. 781 is an irrational number B. 36 is a rational number D. 49 is neither rational nor irrational
The Correct Answer and Explanation is:
Correct Answers:
Question 1:
The square root of 205 lies between 14 and 15.
Answer: D. 14 & 15
Question 2:
Answer: B. 36 is a rational number
Detailed Explanation
Question 1: Between what two consecutive integers does √205 lie?
To find between which two integers √205 lies, consider perfect squares close to 205:
- 14² = 196
- 15² = 225
Now compare:
- √196 = 14
- √225 = 15
- √205 is between 196 and 225
Since 196 < 205 < 225, it means:14<205<1514 < \sqrt{205} < 1514<205<15
Thus, the correct answer is:
D. 14 & 15
We can estimate further:
- Try 14.3² = 204.49
- Try 14.4² = 207.36
So, √205 ≈ 14.3 (which confirms it lies between 14 and 15)
Question 2: Which of the statements is TRUE?
Let’s evaluate each choice:
- A. V is a natural number
This is incomplete or meaningless as “V” is not defined in the question. - B. 36 is a rational number
A rational number is any number that can be expressed as a fraction a/b where a and b are integers and b ≠ 0.
Since 36 = 36/1, it is a rational number.
✅ This is TRUE. - C. 781 is an irrational number
781 is a whole number and can be written as 781/1, so it is rational. ❌ False. - D. 49 is neither rational nor irrational
49 is a whole number (49 = 7²) and therefore rational. ❌ False.
Correct answer: B. 36 is a rational number
Conclusion
- √205 lies between 14 and 15
- The true statement is: 36 is a rational number
