Question Bank: Real Numbers

How can you represent real numbers on a number line?

Discuss the properties of real numbers and how they are classified.

How can you determine if a number is irrational or rational?

Explain the concept of irrational numbers and provide examples.

What is the Fundamental Theorem of Arithmetic and why is it important in the study of real numbers?

Explain the process of finding the square root of a number.

Discuss the concept of real numbers.

How can you represent irrational numbers on a number line?

Differentiate between rational and irrational numbers.

Explain the concept of rational numbers.

What is the Fundamental Theorem of Arithmetic and why is it important in the study of real numbers?

Explain the concept of irrational numbers and provide examples.

How can you determine if a number is irrational or rational?

Discuss the properties of real numbers and how they are classified.

How can you represent real numbers on a number line?

What is the Fundamental Theorem of Arithmetic?

Explain the concept of prime numbers.

Define composite numbers and provide examples.

How can you determine if a number is irrational?

Discuss the properties of irrational numbers.

Explain the concept of rational numbers.

Differentiate between rational and irrational numbers.

How can you represent irrational numbers on a number line?

Discuss the concept of real numbers.

Explain the process of finding the square root of a number.

What is the Fundamental Theorem of Arithmetic and why is it important in the study of real numbers?

Explain the concept of irrational numbers and provide examples.

How can you determine if a number is irrational or rational?

Discuss the properties of real numbers and how they are classified.

How can you represent real numbers on a number line?

Find the HCF and LCM of 6, 72 and 120, using the prime factorisation method.

Express each number as a product of its prime factors: (i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers. (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54

Find the LCM and HCF of the following integers by applying the prime factorisation method. (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25

Given that HCF (306, 657) = 9, find LCM (306, 657).

Check whether 6n can end with the digit 0 for any natural number n

Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers

There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Prove that sqrt of 3 is irrational.

Show that 5– sqrt of 3 is irrational.

Show that 3*(sqrt of 2) is irrational.

Prove that sqrt of 5 is irrational.

Prove that 3 + 2*sqrt of 5  is irrational.

Prove that the following are irrationals : (i) 1/sqrt 2 (ii) 7 *sqrt 5 (iii) 6 + sqrt 2

Which of the following numbers is a prime number?

What is the greatest common divisor (GCD) of 18 and 24?

Which of the following is an example of an irrational number?

According to the Fundamental Theorem of Arithmetic, how can any composite number be expressed?

What is the prime factorization of 100?

Which of the following numbers has a non-terminating repeating decimal expansion?

If a number has a terminating decimal expansion, which of the following must be true?

What is the decimal representation of the fraction 5/8?

Which statement is true about even and odd numbers?

What is the result of applying Euclid's division algorithm to 15 and 4?

If the prime factorization of a number includes 3², 5, and 7, what could be a possible composite number?

Given the number 72, which of the following is a valid statement regarding its prime factorization?

Which of the following represents a non-terminating decimal?

What is the LCM of 8 and 12?

Which of the following is not a property of prime numbers?

When using Euclid's algorithm, what does it mean if the remainder becomes zero?

What does the Fundamental Theorem of Arithmetic state?

The expression of 28 in terms of its prime factors is:

How many prime factors does the number 30 have?

If a composite number has a prime factorization of 3^2 × 5^1, what is its value?

When can a rational number have a non-terminating decimal expansion?

Which of the following numbers is guaranteed to be irrational based on prime factors?

According to the Fundamental Theorem, what guarantees the uniqueness of prime factorization?

If the prime factorization of a number is 2^3 × 3^2 × 5^1, what is its HCF with 30 (2 × 3 × 5)?

Which is a property of the HCF and LCM of two numbers?

What is the relationship between prime factorization and decimal expansions?

How do we prove that √2 is irrational using the Fundamental Theorem of Arithmetic?

What is a result of applying the Fundamental Theorem of Arithmetic?

What is the Fundamental Theorem of Arithmetic?

Which of the following numbers is irrational?

If 3 is a prime number and it divides the square of a number, what can we infer about that number?

What is the classification of the number π?

Which of the following numbers is irrational?

Which statement is true about the sum of two irrational numbers?

What is the relationship between HCF and LCM for any three positive integers p, q, and r?

If x is an irrational number, what can be said about 2x?

Which of the following proves that 5 is an irrational number?

Which of the following pairs of numbers contains both rational and irrational numbers?

If p is a prime number and divides the square of an integer, what conclusion can be made?

How can you express √3 in terms of integers?

Which of these expressions is irrational?

What is the product of an irrational number and a rational number (other than zero)?

What is the correct way to express the LCM of three numbers?

Which of the following proofs is used to show that 2 is irrational?

Which of these is NOT a rational number?

Which of the following is a property of irrational numbers?

Which of the following statements regarding square roots is true?

If you add two irrational numbers, which of the following could be a possible outcome?

Which statement about the numbers 2 and 3 is true?

What is an example of a number that is not irrational?

In the context of irrational numbers, what does it mean if a number is not expressible as a fraction?

Which of the following statements is correct about √5?

How can you prove that 325 + 1 is irrational?

What does the Fundamental Theorem of Arithmetic state about prime numbers?

Which of the following pairs involves irrational numbers?

Which of the following is true for irrational numbers when expressed in decimal form?

Which of the following is a correct mathematical notation to express the set of irrational numbers?

If x is an irrational number, what is x²?

What is one of the consequences of assuming that √2 is rational?