√2 is the irrational number listed while 22/7, √4 and 0.333 stay rational, so this Class 9 sheet opens by sorting the number types on the real line. The decimal of 17/8 is terminating, with 3/8 and √2/2 among the later answers.
Key Takeaways
√2 is an irrational number (Q1).
The decimal expansion of 17/8 is terminating (Q2).
Q3 records 3/8 among the answers.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.Which of the following is an irrational number?
(a) 22/7(b) √4(c) √2(d) 0.333
2.The decimal expansion of 17/8 is
(a) Terminating(b) Non-terminating repeating(c) Non-terminating non-repeating(d) Cannot be determined
3.Which number has a terminating decimal expansion?
(a) 1/3(b) 1/7(c) 3/8(d) 1/6
4.The value of (√5 + √2)(√5 - √2) is
(a) 3(b) 7(c) 5 - 2√10(d) 10
5.On rationalising the denominator of 1/√2, we get
(a) √2/2(b) √2(c) 2/√2(d) 1/√2
6.If x = 2 + √3, then 1/x is equal to
(a) 2 + √3(b) 2 - √3(c) -2 + √3(d) -2 - √3
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Write the simplest rationalising factor of √5.
8.State whether 0 is a rational number or not.
9.Classify √23 as rational or irrational.
10.Express 0.6 (where 6 repeats) in the form p/q, where p and q are integers.
11.Simplify √50 - √18.
12.Express 5.23 (where 23 repeats) in the form p/q.
13.Find two rational numbers between 2 and 3.
14.If √2 = 1.414, find the value of √8.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.The area of a square is 18 cm². Express the length of its side in the simplest surd form and find the perimeter of the square.
16.Sita walks √50 km to school and √32 km back home every day. Find the total distance she walks in a week (7 days) in the simplest surd form.
17.A rectangular garden is √125 m long and √20 m wide. Find the area of the garden.
18.A rope of length √98 m is cut into 7 equal pieces. Find the length of each piece in the simplest surd form.
19.The area of a rectangle is 5 cm² and one of its sides is √5 cm. Find the length of the other side.
20.Taking √3 = 1.732, find the value of √12 + √27 correct to two decimal places.
Answer Key
1. c) √2
2. a) Terminating
3. c) 3/8
4. a) 3
5. a) √2/2
6. b) 2 - √3
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
Which of these is an irrational number?
√2, option (c) in this worksheet (Q1).
What kind of decimal does 17/8 have?
A terminating decimal, option (a) in this worksheet (Q2).
What is the value of 0.375 as a fraction?
3/8, option (c) in this worksheet (Q3).
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