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Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.
CAN U EXPLAIN THIS PLEASE?
CAN U EXPLAIN THIS PLEASE?
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Q9. How many numbers lie between squares of the following numbers? (i)...
Understanding the Concept of Numbers Between Squares
To find how many numbers lie between the squares of two consecutive integers, we can use a simple formula. The formula states that the count of non-square numbers between n² and (n + 1)² is given by 2n. Here's a breakdown of how this works:
Why Use the Formula?
- The squares of two consecutive integers are calculated as follows:
- n² (square of n)
- (n + 1)² (square of the next integer)
- The difference between these two squares can be calculated:
- (n + 1)² - n² = 2n + 1
- This means there are 2n + 1 total numbers between these two squares, but we need to exclude the two square numbers (n² and (n + 1)²).
- Thus, the count of non-square numbers is:
- Total numbers - 2 (the squares themselves) = (2n + 1) - 2 = 2n.
Applying the Formula to Examples
Now, let's apply this formula to the specific examples given:
(i) Between 12 and 13
- n = 12
- Calculation: 2 * 12 = 24
- There are 24 non-square numbers between 12² (144) and 13² (169).
(ii) Between 25 and 26
- n = 25
- Calculation: 2 * 25 = 50
- There are 50 non-square numbers between 25² (625) and 26² (676).
(iii) Between 99 and 100
- n = 99
- Calculation: 2 * 99 = 198
- There are 198 non-square numbers between 99² (9801) and 100² (10000).
Conclusion
Using this method, you can easily determine how many numbers lie between the squares of any two consecutive integers. This concept is useful in number theory and can enhance your understanding of the relationships between numbers and their properties.
To find how many numbers lie between the squares of two consecutive integers, we can use a simple formula. The formula states that the count of non-square numbers between n² and (n + 1)² is given by 2n. Here's a breakdown of how this works:
Why Use the Formula?
- The squares of two consecutive integers are calculated as follows:
- n² (square of n)
- (n + 1)² (square of the next integer)
- The difference between these two squares can be calculated:
- (n + 1)² - n² = 2n + 1
- This means there are 2n + 1 total numbers between these two squares, but we need to exclude the two square numbers (n² and (n + 1)²).
- Thus, the count of non-square numbers is:
- Total numbers - 2 (the squares themselves) = (2n + 1) - 2 = 2n.
Applying the Formula to Examples
Now, let's apply this formula to the specific examples given:
(i) Between 12 and 13
- n = 12
- Calculation: 2 * 12 = 24
- There are 24 non-square numbers between 12² (144) and 13² (169).
(ii) Between 25 and 26
- n = 25
- Calculation: 2 * 25 = 50
- There are 50 non-square numbers between 25² (625) and 26² (676).
(iii) Between 99 and 100
- n = 99
- Calculation: 2 * 99 = 198
- There are 198 non-square numbers between 99² (9801) and 100² (10000).
Conclusion
Using this method, you can easily determine how many numbers lie between the squares of any two consecutive integers. This concept is useful in number theory and can enhance your understanding of the relationships between numbers and their properties.
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Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE?
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Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE?.
Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE?.
Solutions for Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE? in English & in Hindi are available as part of our courses for Class 8.
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Here you can find the meaning of Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE? defined & explained in the simplest way possible. Besides giving the explanation of
Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE?, a detailed solution for Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE? has been provided alongside types of Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE? theory, EduRev gives you an
ample number of questions to practice Q9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 Solution: Since between n2 and (n + 1)2, there are 2n non-square numbers. (i) Between 122 and 132, there are 2 *12, i.e. 24 numbers. (ii) Between 252 and 262, there are 2 * 25, i.e. 50 numbers. (iii) Between 992 and 1002, there are 2 * 99, i.e. 198 numbers.CAN U EXPLAIN THIS PLEASE? tests, examples and also practice Class 8 tests.
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