What is rational number ?
All numbers that can be written in the form of p/q is rational number.
What are irrational numbers ?
The numbers that cannot be written in the form of fraction, those are irrational numbers.
Compare the following numbers using < or >.
Problem 1 :
√32 ___ 5.1
Solution :
√32 ___5.1
√32 lies between √25 and √36.
5.1 is nearer to 5, so value of √32 will be greater than 5.1.
√32 > 5.1
Problem 2 :
√38 ____√42
Solution :
√38 ___√42
√38 lies between √36 and √49.
√38 < √42
Problem 3 :
√17___ 9/2
Solution :
√17____ 9/2
√17 lies between √16 and √25.
√16 = 4, then approximate value of √17 is 4.1...
9/2 = 4.5
4.1 < 4.5
√17 < 9/2
Problem 4 :
√49___ 7.1
Solution :
√49___7.1
√49 = √(7 × 7)
= 7
7 < 7.1
√49 < 7.1
Problem 5 :
√99 ____ 28/3
Solution :
√99 ____ 28/3
√99 lies between √81 and √100.
√99 is nearly √100, so approximate value of √99 is 9.9...
28/3 = 9.33
9.9 > 9.33
√99 > 28/3
Problem 6 :
√17 ___ 4.5
Solution :
√17 ____ 4.5
√17 lies between √16 and √25.
So, approximate value of √17 is 4.1...
4.1 < 4.5
√17 < 4.5
Problem 7 :
43/5 _____√65
Solution :
43/5 ____ √65
43/5 = 8.6
√65 lies between √64 and √81.
√65 is nearly √64. So, its approximate value will be 8.1.....
8.6 > 8.062
43/5 > √65
Problem 8 :
√12 ___√21
Solution :
√12 ____√21
√12 lies between √9 and √16.
So, approximate value of √12 is 3.....
√21 lies between √16 and √25.
So, approximate value of √21 is 4.....
3.464 < 4.582
√12 < √21
Problem 9 :
√16 ___ 3.9
Solution :
√16 ___ 3.9
√16 = √(4 × 4)
= 4
4 > 3.9
Problem 10 :
√2 ___ 7/4
Solution :
√2 ___ 7/4
√2 lies between √1 and √3.
Approximate values of √2 is 1.414.
7/4 = 1.75
1.414 < 1.75
Problem 11 :
√50 ___15/2
Solution :
√50 ___ 15/2
√50 lies between √49 and √64.
Approximate values of √50 is 7.07.
15/2 = 7.5
7.07 < 7.5
Problem12 :
√9 ____3.01
Solution :
√9 ___3.01
√9 = √(3 × 3)
= 3
3 < 3.01
√9 < 3.01
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM