..hi friends, i need many sums on the chapter rational number and exponents and power for grade 8th atleast above 55 question for each chapter which i mentioned (please give some questions )thanks sister kiara1187
Answers
Answer:
1.State whether the following statements are true or false. Give reason for you
answers.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.
1) Write four rational numbers equivalent to 5 /7
.
2) Find four rational numbers between 3 /4
and 2 /5
3) Find nine rational numbers between 0.1 and 0.2.
4) Find five rational numbers 2 and 1.
5) Find four rational numbers between 2 /3
and 3 /5
6.State whether the following statements are true or false. Justify your answers.
(i) Every irrational number is a real number.
(ii) Every point on the number line is of the form √m, where m is a natural
number.
(iii) Every real number is an irrational number.
Are the square roots of all positive integers irrational? If not, give an example of
7.The square root of a number that is a rational number.
8.Represent √2 on the number line.
9.Represent √3 on the number line.
10. Construct a “ Square-root spiral ” depicting √2, √3,√4,√5, √6....also
represent √2, √3,√4,√5, √6 on the real line.
11.Write the following in decimal form and say what kind of decimal expansion each
has:
(i) 36 /100
(ii) 1 /11
(iii) 4 1 /8
(iv) 3 /13
(v) 2 /11
(vi) 329 /400
12.
(i) 0.6
(ii) 0.47
(iii) 0.001
13.What can the maximum number of digits be in the repeating block of digits in the decimal expansions of 1 /17 ? Perform the division to check your answer.
14.Look at several examples of rational numbers in the form p /q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?
15.Write three numbers whose decimal expansions are non-terminating non- recurring.
16.Classify the following numbers as rational or irrational:
(i) √23
(ii) √225
(iii) 0.3796
(iv) 7.478478
(v) 1.101001000100001.......
Express 0.38383838..... as a rational number in simplest form.
Express 0.5353535353... in the form of p /q .
Express 0.003003003003... in the form of p/q .in the simplest form.
16.Represent √3.5 on the number line.
17.Visualise 4.26 on the number line, up to 4 decimal places.
18.Classify the following numbers as rational or irrational:
(i) 2 − √5
(ii) (3 + √23) − √23
(iii) 2√7 /7√7
(iv) 1 /√2
(v)2π
19.Simplify the following expressions:
(iii) (√5 + √2) ^2
(iv) (√5 − √2)(√5 + √2)
(v) (5 + √7)(2 + √5)
(vi) (5 + √5)(5 − √5)
(vii) (√3 + √7) ^2
(viii) (√11 − √7)(√11 + √7)
20.Rationalise the denominators of the following:
21. 1 /√7
22.1 /√7−√6
23.Add (√2 − 3√3) and (2√2 + 5√3)
24. Find the product of 2√5 and 6√5
25 Divide 16√15 by 4√3
26. If a − b√3 = 2−√3 /2+√3 , then find the value of ‘a’ and ‘b’
27. If x = 2 + √3, then find the value of x ^2 + 1/x^2
Choose an appropriate answer for each of the following:
1. Which is the smallest natural number?
a) 0 b) 1 c) 2
2. Which is the smallest whole number?
a) 0 b) 1 c) 2
3. Which is the smallest positive integer?
a) 0 b) 1 c) −1
4. Which is the greatest negative integer?
a) 0 b) 1 c) −1
5. Which integer is neither negative nor positive?
a) 0 b) 1 c) 2
6. A number which cannot be written in the form of p /q (q ≠ 0) is called a
a) Rational number
b) Whole number
c) Irrational number
7. How many real numbers can exist between any two real numbers?
a) None c) Infinite numbers of real number
b) Only one
8. π and 22 /7 are same up to how many places of decimal?
a) One c) Infinite numbers of real number
b) b) Two
9. √2 is a
a) Whole number
b) Rational number
c) Irrational number
10. What is the value of (2 ^3)^2 ?
a) 32
b) 16
c) 64
Answer the following: (2 marks)
11. Find a rational number between 1 and 2.
12.Write a rational number equivalent to 5 /9 such that its numerator is 25.
13.Find two rational numbers between 0.1 and 0.3.
14.Express 3 1 /8 in the form of decimal.
15.Express 0.33 as a rational number.
16.Simplify (4 + √3)(4 − √3)
17.Simplify (√3 + √2) ^2
18.Rationalise the denominator of 1 /√3−√2
19.Find (64) ^(−1/ 3 )
Answer the following: (3 marks)
20.Find a rational number lying between 1 /5 and 1 /2
21.Find three rational numbers between 0 and 0.1
22.Express 0.245245245245....... as a fraction in the simplest form.
23.If x = (2 + √5), find the value of (x ^2 + 1 /x ^2 )
24.Find the value of (x + 1^/x ) when x = (4 − √15)
25.Find the value of (x ^2 + 1 /x ^2 ) when x = (2 + √3)
26.Simplify (5+√5)(5−√5) /(3+√2)(3−√2)
Answer the following: (4 marks)
27.Find six rational numbers between 1 and 2.
28.Find five rational numbers between 0.6 and 0.8
29.If ‘a’ and ‘b’ are rational numbers and 3+√8 /3−√8 = a + b√8 , then find the value of ‘a’ and ‘b’.
30. If ‘a’ and ‘b’ are rational numbers and 3+3√2 /3−3√2 = a + b√2 , then find the value of ‘a’ and ‘b’.
31. Show that (√3−√2 /√3+√2 )+ (√3+√2 /√3−√2 )= 10
32.Find the nine rational numbers between 0 and 0.1.
I have tried my best. Hope it helps you☺.........
P.S it took me half an hour to find these questions.....
Answer:
write 0.5353535353 in form of rational