Worksheet: Real Numbers

# Real Numbers Class 10 Worksheet Maths Chapter 1

True and False

Q1: State whether the given statement is true or false :
(i) The product of two rationals is always rational

(ii) The product of two irrationals is an irrational
(iii) The product of a rational and an irrational is irrational
(iv) The sum of two rationals is always rational
(v) The sum of two irrationals is an irrational.

Very Short Questions
Q.2. Classify the following numbers as rational or irrational:
(i) 3.1416
(ii) 3.142857
(iii) 2.040040004......
(iv) 3.121221222...
(v) 3√3

Q.3. Find the prime factorization of 1152

Q4: Show that the product of two numbers 60 and 84 is equal to the product of their HCF and LCM

Q5: If p and q are two coprime numbers, then find the HCF and LCM of p and q.

Short Questions
Q6: Given that H.C.F. (306, 657) = 9, find L.C.M. (306, 657)

Q7: The H.C.F. and L.C.M. of two numbers are 12 and 240 respectively. If one of these numbers is 48; find the other numbers.

Long Questions

Q8: Use Euclid’s Division Algorithm to show that the cube of any positive integer is either of the 9m, 9m + 1 or 9m + 8 for some integer m.

Q9: Show that any positive integer which is of the form 6q + 1 or 6q + 3 or 6q + 5 is odd, where q is some integer.

Q10: Prove that
(i) √2 is irrational number
(ii) √3 is irrational number
Similarly √5, √7, √11…... are irrational numbers.

You can find Worksheets Solutions here: Worksheet Solutions: Real Numbers

The document Real Numbers Class 10 Worksheet Maths Chapter 1 is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10

## Mathematics (Maths) Class 10

126 videos|477 docs|105 tests

## FAQs on Real Numbers Class 10 Worksheet Maths Chapter 1

 1. What are real numbers?
Ans. Real numbers are numbers that can be found on the number line. They include all rational and irrational numbers, such as whole numbers, fractions, decimals, and square roots.
 2. How are real numbers different from imaginary numbers?
Ans. Real numbers represent quantities that exist in the real world and can be measured, while imaginary numbers involve the square root of negative numbers and are used in complex numbers. Real numbers have a real part, while imaginary numbers have an imaginary part.
 3. Can a real number be negative?
Ans. Yes, real numbers can be both positive and negative. They can be located to the left or right of zero on the number line. Positive real numbers are greater than zero, while negative real numbers are less than zero.
 4. Are all integers real numbers?
Ans. Yes, all integers are real numbers. Integers are whole numbers, either positive, negative, or zero. They can be plotted on the number line and are part of the set of real numbers.
 5. What is the difference between rational and irrational numbers?
Ans. Rational numbers can be expressed as a fraction or ratio of two integers, while irrational numbers cannot be expressed as a fraction and have non-repeating decimal representations. Rational numbers can be terminated or recurring decimals, while irrational numbers have infinite non-repeating decimal expansions.

## Mathematics (Maths) Class 10

126 videos|477 docs|105 tests

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