IDNLearn.com connects you with a community of experts ready to answer your questions. Join our community to receive prompt and reliable responses to your questions from experienced professionals.
Sagot :
Certainly! Let me walk you through each part of the question step-by-step.
### (i) Suraj's Question: About \(\sqrt{8}\)
Question: Which of the following is true about \(\sqrt{8}\)?
Options are:
1. (a) It is a natural number
2. (b) It is an irrational number
3. (c) It is a rational number
4. (d) None of these
Solution:
- A natural number is a positive integer: \(\sqrt{8}\) is not a natural number.
- A rational number can be expressed in the form \(\frac{p}{q}\) where \(p\) and \(q\) are integers and \(q \neq 0\): \(\sqrt{8}\) cannot be expressed this way as it cannot be simplified to a fraction with integer components.
- Since \(\sqrt{8}\) is not rational, it must be irrational.
Answer: (b) It is an irrational number
### (ii) Shreya's Question: About Which is Not Irrational
Question: Which of the following is not irrational?
Options are:
1. (a) \(3 - 4\sqrt{5}\)
2. (b) \(\sqrt{7} - 6\)
3. (c) \(2 + 2\sqrt{9}\)
4. (d) \(4\sqrt{11} - 6\)
Solution:
- \(3 - 4\sqrt{5}\) involves the irrational number \(\sqrt{5}\) making it irrational.
- \(\sqrt{7} - 6\) involves the irrational number \(\sqrt{7}\) making it irrational.
- \(2 + 2\sqrt{9} = 2 + 2 \times 3 = 2 + 6 = 8\) which is a rational number.
- \(4\sqrt{11} - 6\) involves the irrational number \(\sqrt{11}\) making it irrational.
Answer: (c) \(2 + 2\sqrt{9}\)
### (iii) Ananya's Question: About \(\sqrt{15} - \sqrt{10}\)
Question: \(\sqrt{15} - \sqrt{10}\) is ______ number.
Options are:
1. (a) a natural
2. (b) an irrational
3. (c) a whole
4. (d) a rational
Solution:
- The difference between two irrational numbers is typically irrational unless they cancel out perfectly, which they do not in this case.
Answer: (b) an irrational
### (iv) Suman's Question: About \(\frac{1}{\sqrt{5}}\)
Question: \(\frac{1}{\sqrt{5}} \) is ______ number.
Options are:
1. (a) a whole
2. (b) a rational
3. (c) an irrational
4. (d) a natural
Solution:
- \(\sqrt{5}\) is an irrational number, and dividing 1 by an irrational number remains irrational.
Answer: (c) an irrational
### (v) Preethi's Question: About \(\sqrt{6}\)
Question: Which of the following is not irrational?
Options are:
1. (a) \(15 + 3\sqrt{6}\)
2. (b) \(\sqrt{24} - 9\)
3. (c) \(5\sqrt{150}\)
4. (d) None of these
Solution:
- Each of the given options involves an irrational number component, thus all mentioned expressions are irrational.
Answer: (d) None of these
Summarizing the answers:
1. (i) (b) It is an irrational number
2. (ii) (c) \(2 + 2\sqrt{9}\)
3. (iii) (b) an irrational
4. (iv) (c) an irrational
5. (v) (d) None of these
These are the correct solutions.
### (i) Suraj's Question: About \(\sqrt{8}\)
Question: Which of the following is true about \(\sqrt{8}\)?
Options are:
1. (a) It is a natural number
2. (b) It is an irrational number
3. (c) It is a rational number
4. (d) None of these
Solution:
- A natural number is a positive integer: \(\sqrt{8}\) is not a natural number.
- A rational number can be expressed in the form \(\frac{p}{q}\) where \(p\) and \(q\) are integers and \(q \neq 0\): \(\sqrt{8}\) cannot be expressed this way as it cannot be simplified to a fraction with integer components.
- Since \(\sqrt{8}\) is not rational, it must be irrational.
Answer: (b) It is an irrational number
### (ii) Shreya's Question: About Which is Not Irrational
Question: Which of the following is not irrational?
Options are:
1. (a) \(3 - 4\sqrt{5}\)
2. (b) \(\sqrt{7} - 6\)
3. (c) \(2 + 2\sqrt{9}\)
4. (d) \(4\sqrt{11} - 6\)
Solution:
- \(3 - 4\sqrt{5}\) involves the irrational number \(\sqrt{5}\) making it irrational.
- \(\sqrt{7} - 6\) involves the irrational number \(\sqrt{7}\) making it irrational.
- \(2 + 2\sqrt{9} = 2 + 2 \times 3 = 2 + 6 = 8\) which is a rational number.
- \(4\sqrt{11} - 6\) involves the irrational number \(\sqrt{11}\) making it irrational.
Answer: (c) \(2 + 2\sqrt{9}\)
### (iii) Ananya's Question: About \(\sqrt{15} - \sqrt{10}\)
Question: \(\sqrt{15} - \sqrt{10}\) is ______ number.
Options are:
1. (a) a natural
2. (b) an irrational
3. (c) a whole
4. (d) a rational
Solution:
- The difference between two irrational numbers is typically irrational unless they cancel out perfectly, which they do not in this case.
Answer: (b) an irrational
### (iv) Suman's Question: About \(\frac{1}{\sqrt{5}}\)
Question: \(\frac{1}{\sqrt{5}} \) is ______ number.
Options are:
1. (a) a whole
2. (b) a rational
3. (c) an irrational
4. (d) a natural
Solution:
- \(\sqrt{5}\) is an irrational number, and dividing 1 by an irrational number remains irrational.
Answer: (c) an irrational
### (v) Preethi's Question: About \(\sqrt{6}\)
Question: Which of the following is not irrational?
Options are:
1. (a) \(15 + 3\sqrt{6}\)
2. (b) \(\sqrt{24} - 9\)
3. (c) \(5\sqrt{150}\)
4. (d) None of these
Solution:
- Each of the given options involves an irrational number component, thus all mentioned expressions are irrational.
Answer: (d) None of these
Summarizing the answers:
1. (i) (b) It is an irrational number
2. (ii) (c) \(2 + 2\sqrt{9}\)
3. (iii) (b) an irrational
4. (iv) (c) an irrational
5. (v) (d) None of these
These are the correct solutions.
We are delighted to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.
