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?

What does the Fundamental Theorem of Arithmetic state?

Which of the following is true regarding the number 36?

If a number can be expressed as a product of primes, what does this imply?

What is the prime factorization of 60?

Which of the following is NOT a valid application of the Fundamental Theorem of Arithmetic?

What statement about the prime factorization of composite numbers is correct?

If 2^3 × 3 × 5 represents a number, what number is represented?

Using the Fundamental Theorem of Arithmetic, if a composite number is divisible by both 2 and 3, what can we say about its prime factorization?

If a number is expressed as a product of primes 5 × 5 × 2, what is its square?

When can the decimal expansion of a fraction be non-terminating?

Using the Fundamental Theorem of Arithmetic, which statement about the number 18 is true?

What is the result of the product of the HCF and LCM of two numbers?

Which of the following is a rational number?

If a natural number n is expressed as a product of primes where one of the prime factors is 7, what can be inferred?

What is the decimal expansion of 1/8?

Euclid’s division algorithm is primarily used to find which of the following?

According to the Fundamental Theorem of Arithmetic, every composite number can be expressed as:

What will be the decimal representation of 1/6?

Which of the following numbers is NOT an integer?

If the prime factorization of a number is 2^3 × 5^1, what is the number?

The decimal representation of 2/5 is:

What is the smallest prime number?

Which of the following numbers is irrational?

Which of the following best describes a non-terminating decimal?

What is the HCF of 48 and 60 using Euclid's algorithm?

Which statement is true about rational numbers?

Find the prime factorization of 60.

Which of the following fractions has a terminating decimal when expressed?

What is the Euclidean algorithm used for?

Identify the product of 3 and 5 using their prime factor representations.

Which of the following numbers is irrational?

According to the Fundamental Theorem of Arithmetic, what can every composite number be expressed as?

If 5 is a prime number and it divides a², what can we conclude about a?

Which of the following sums is guaranteed to be irrational?

What is the greatest common divisor (HCF) of 12 and 15?

What is the least common multiple (LCM) of 4 and 5?

How is LCM related to HCF for three numbers?

What is the value of √(-1)?

Which of the following is NOT an irrational number?

If a number is expressed as a sum of a rational number and an irrational number, what is the type of the result?

Which of the following statements is true about composite numbers?

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

To prove that √5 is irrational, which of the following methods is commonly used?

What property defines an irrational number?

For the numbers 8, 12, and 20, what is their HCF?

Which of the following statements is true for √2?

Which statement is true regarding the decimal expansion of irrational numbers?

How can you prove that √5 is irrational?

What can be concluded if an integer a is divided by a prime number p?

If a rational number is expressed as a decimal, what will it be like?

What type of number is always a factor of any integer?

Which of the following roots is irrational?

What is the value of √(2) + √(2) - √(2)?

Which of the following statements about irrational numbers is false?

If √p is irrational, which of the following must be true?

Which number can be expressed as a sum of a rational and an irrational number?

Using the proof by contradiction method, which assumption leads to the conclusion that √2 is irrational?

Which of the following pairs includes a rational and an irrational number?

The decimal expansion of which of the following is characterized as non-terminating and non-repeating?

Why is √10 considered irrational?

What is a common misconception about irrational numbers?

What is the prime factorization of 60?

What is the HCF of 48 and 180?

Which of the following numbers is irrational?

Identify a rational number from the list below.

What is the LCM of 12 and 15?

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

Determine if the following statement is true: The product of HCF and LCM of two numbers equals the product of the numbers.

If p is a prime number and divides a^2, what can you conclude about p and a?

What is the decimal representation of 2/3?

Which of the following is a non-terminating decimal?

Why does a number with a prime factor of 2 in the denominator lead to a terminating decimal?

Which statement about irrational numbers is correct?

If the decimal representation of a rational number is terminating, which of the following must be true about its denominator?

Which of the following is a correct implication of the Fundamental Theorem of Arithmetic?

Prove that an irrational number plus a rational number is irrational.

Determine if √6 is irrational.