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If 'a' and 'b' are coprime, then 'a square' and 'b square' are: (A) Even number (B)Co prime (C)Odd number (D)No coprime?
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If 'a' and 'b' are coprime, then 'a square' and 'b square' are: (A) Ev...
Correct answer is is B because if you take two coprime numbers
Example -> 2 and 3 and if we square the digits we get 4 and 9 which is again a coprime number.
Example -> 2 and 3 and if we square the digits we get 4 and 9 which is again a coprime number.
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If 'a' and 'b' are coprime, then 'a square' and 'b square' are: (A) Ev...
Answer:
Coprime numbers:
When two numbers have no common factors other than 1, they are known as co-prime or relatively prime numbers. In other words, two integers are co-prime if their greatest common divisor is 1.
Squares of coprime numbers:
If 'a' and 'b' are co-prime, then it means that they have no common factors other than 1. In that case, the squares of 'a' and 'b' will also have no common factors other than 1.
Option (B)Co prime:
Therefore, the correct answer to the given question is option (B) Co prime.
Explanation:
Let's understand this with an example:
Suppose 'a' and 'b' are co-prime numbers. Therefore, their greatest common divisor (GCD) will be 1.
Let's say:
a = 5
b = 7
Now, we need to find the squares of 'a' and 'b':
a^2 = 5^2 = 25
b^2 = 7^2 = 49
As we can see, the squares of 'a' and 'b' are 25 and 49 respectively. Both of these numbers are prime and have no common factors other than 1. Therefore, they are also co-prime.
Hence, we can conclude that if 'a' and 'b' are co-prime, then their squares will also be co-prime.
Coprime numbers:
When two numbers have no common factors other than 1, they are known as co-prime or relatively prime numbers. In other words, two integers are co-prime if their greatest common divisor is 1.
Squares of coprime numbers:
If 'a' and 'b' are co-prime, then it means that they have no common factors other than 1. In that case, the squares of 'a' and 'b' will also have no common factors other than 1.
Option (B)Co prime:
Therefore, the correct answer to the given question is option (B) Co prime.
Explanation:
Let's understand this with an example:
Suppose 'a' and 'b' are co-prime numbers. Therefore, their greatest common divisor (GCD) will be 1.
Let's say:
a = 5
b = 7
Now, we need to find the squares of 'a' and 'b':
a^2 = 5^2 = 25
b^2 = 7^2 = 49
As we can see, the squares of 'a' and 'b' are 25 and 49 respectively. Both of these numbers are prime and have no common factors other than 1. Therefore, they are also co-prime.
Hence, we can conclude that if 'a' and 'b' are co-prime, then their squares will also be co-prime.
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If 'a' and 'b' are coprime, then 'a square' and 'b square' are: (A) Even number (B)Co prime (C)Odd number (D)No coprime?
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If 'a' and 'b' are coprime, then 'a square' and 'b square' are: (A) Even number (B)Co prime (C)Odd number (D)No coprime? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 'a' and 'b' are coprime, then 'a square' and 'b square' are: (A) Even number (B)Co prime (C)Odd number (D)No coprime? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 'a' and 'b' are coprime, then 'a square' and 'b square' are: (A) Even number (B)Co prime (C)Odd number (D)No coprime?.
If 'a' and 'b' are coprime, then 'a square' and 'b square' are: (A) Even number (B)Co prime (C)Odd number (D)No coprime? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If 'a' and 'b' are coprime, then 'a square' and 'b square' are: (A) Even number (B)Co prime (C)Odd number (D)No coprime? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 'a' and 'b' are coprime, then 'a square' and 'b square' are: (A) Even number (B)Co prime (C)Odd number (D)No coprime?.
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