Question Bank: Real Numbers

What is the prime factorization of 140?

Which of the following is a composite number?

If a number can be expressed as a product of its prime factors, what is it called?

Which of the following statements is true according to the Fundamental Theorem of Arithmetic?

What is the HCF of 24 and 36 using prime factorization?

What is the prime factorization of 60?

When does a decimal expansion of a rational number terminate?

If a composite number has a prime factorization of 2³ × 3¹ × 5², what is one of its factors?

Which of the following numbers is irrational?

Which of the following numbers is NOT a prime factor of 45?

What is the LCM of 8 and 12?

What is the least common multiple (LCM) of 12 and 15 using their prime factorization?

Given that HCF(18, 24) = 6, find LCM(18, 24).

For which value of n does 6^n end in 0?

How is the prime factorization of 60 represented?

Which pair of numbers has the same prime factors?

What is √75 expressed in simplest form?

Which number cannot be expressed as a product of prime numbers according to the Fundamental Theorem of Arithmetic?

What is the product of HCF and LCM of two numbers equal to?

If the prime factorization of a number is of the form p^a × q^b where p and q are primes, what can be said about it?

If p is a prime factor of n², what can be inferred about n?

Which of the following is true regarding irrational numbers?

Which of the following numbers is irrational?

Which equation demonstrates that √2 is irrational?

Which of the following is a true application of the Fundamental Theorem of Arithmetic?

The number 44 can be factored as 2² × 11. What is one possible composite number formed using these prime factors?

How many distinct prime factors does the number 126 have?

Can a composite number exist with only one prime factor?

What is a real number?

Which of the following is NOT a real number?

Which statement about the Fundamental Theorem of Arithmetic is true?

In the context of Euclid's division algorithm, if a = 17 and b = 5, what is the remainder?

When does the decimal expansion of a rational number terminate?

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

How can you find the HCF of 48 and 180 using Euclid's division algorithm?

The expression √3 is an example of which type of number?

What does the geometric representation of real numbers depict?

Which of the following is true regarding rational numbers?

If p = 12 and q = 18, what is the HCF of p and q?

What does Euclid's Division Algorithm state about two positive integers 'a' and 'b'?

Which of the following numbers is NOT a prime number?

If 50 is divided by 8, what is the remainder according to Euclid's Algorithm?

How does one represent a non-repeating decimal?

Which of the following represents the correct equation based on Euclid's Division Algorithm?

How can Euclid's Division Algorithm be used to find the HCF of two numbers?

What is the decimal equivalent of the fraction 3/8?

Using Euclid's algorithm, what is the HCF of 56 and 98?

What property does Euclid's algorithm demonstrate?

If a = 70 and b = 35, what is the remainder when a is divided by b using Euclid's algorithm?

What is the first prime factor of 60?

If a number is expressed as p/q where q = 10, what is its decimal nature?

What is the main advantage of using Euclid's Division Algorithm?

Which step correctly follows Euclid's Division Algorithm process for finding HCF?

What is the HCF of 24 and 36 using Euclid's Division Algorithm?

In applying Euclid's Division Algorithm to find HCF, which equation is used?

If the remainder when dividing 90 by 11 is 2, what can you conclude using Euclid's Theorem?

Using Euclid's algorithm, what is the HCF of 81 and 27?

For two numbers 144 and 60, what is one of the stages in using Euclid's algorithm?

Using Euclid's algorithm, what is the first remainder when finding the HCF of 54 and 24?

Which of the following numbers is irrational?

What is the value of √2 + √3?

Can √18 be expressed as a simple fraction?

If a rational number is added to √2, what will the result be?

What type of number is √-4?

Which of the following represents an irrational number?

How is √5 categorized?

If a number is both rational and irrational, what can be concluded?

Which statement about irrational numbers is true?

What defines an irrational number?

Which of the following sums results in an irrational number?

Which expression is definitely irrational?

Prove that √3 is irrational using what theorem?

Which statement about squares of irrational numbers is correct?

Is it possible for a rational number and an irrational number to multiply to a rational number?

What can we conclude about the roots of prime numbers?

Confirm the result of √2 + √3. What does it signify?