Question 1 :
Compare 5√3 and 7√2 and write <, >, or = in between them.
Question 2 :
Compare 4√5 and 3√10 and write < or > between them.
Question 3 :
Compare 2√3 and √12 and write <, >, or = in between them.
Question 4 :
Compare √5 and (2 + √3) and write < or > between them.
Question 5 :
Compare (√2 + 3) and (2 + √3) and write <, >, or = in between them.
Question 6 :
Compare (√10 - 1) and (√5 + 1) and write <, >, or = in between them.
Question 7 :
Compare (√5 + 6) and (√6 + 5) and write <, >, or = in between them.
Question 8 :
Compare (√2 - 1) and (√10 - 2) and write <, >, or = in between them.
Question 9 :
Compare (√2 + 5) and (√5 + 2) and write <, >, or = in between them.
Question 10 :
Compare (√15 - 2) and (1 + √3) and write <, >, or = in between them.
Question 11 :
Compare 𝝅 and √2 and and write <, >, or = in between them.
Question 12 :
Compare (1 + √3) and (1 + 𝝅) and write <, >, or = in between them.
Question 13 :
Compare (𝝅 + 2) and (e + 2) and write <, >, or = in between them.
1. Answer :
Step 1 :
Square 5√3.
(5√3)^{2} = 5^{2}(√3)^{2}
= 25(3)
= 75 ----(1)
Step 2 :
Square 7√2.
(7√2)^{2} = 7^{2}(√2)^{2}
= 49(2)
= 98 ----(2)
Step 3 :
Comparing (1) and (2),
75 < 98 ----> 5√3 > 7√2
2. Answer :
Step 1 :
Square 4√5.
(4√5)^{2} = 4^{2}(√5)^{2}
= 16(5)
= 80 ----(1)
Step 2 :
Square 3√10.
(3√10)^{2} = 3^{2}(√10)^{2}
=9(10)
= 90 ----(2)
Step 3 :
Comparing (1) and (2),
80 < 90 ----> 4√5 < 3√10
3. Answer :
Step 1 :
Square 2√3.
(2√3)^{2} = 2^{2}(√3)^{2}
= 4(3)
= 12 ----(1)
Step 2 :
Square √12.
(√12)^{2} = 12 ----(2)
Step 3 :
Comparing (1) and (2),
12 = 12 ----> 2√3 = √12
4. Answer :
Step 1 :
Approximate √5.
√5 is between 2 and 3 ----(1)
Step 2 :
Approximate (2 + √3).
√3 is between 1 and 2
(2 + √3) is between 3 and 4 ----(2)
Step 3 :
Comparing (1) and (2),
√5 < (2 + √3)
5 Answer :
Step 1 :
Approximate (√2 + 3).
√2 is between 1 and 2
(√2 + 3) is between 4 and 5 ----(1)
Step 2 :
Approximate (2 + √3).
√3 is between 1 and 2
(2 + √3) is between 3 and 4 ----(2)
Step 3 :
Comparing (1) and (2),
(√2 + 3) > (2 + √3)
6. Answer :
Step 1 :
Approximate (√10 - 1).
√10 is between 3 and 4
(√10 - 1) is between 2 and 3 ----(1)
Step 2 :
Approximate (√5 + 1).
√5 is between 2 and 3
(√5 + 1) is between 3 and 4 ----(2)
Step 3 :
Comparing (1) and (2),
(√10 - 1) < (√5 + 1)
7. Answer :
Step 1 :
Approximate (√5 + 6).
√5 is between 2 and 3
(√5 + 6) is between 8 and 9 ----(1)
Step 2 :
Approximate (√6 + 5).
√6 is between 2 and 3
(√6 + 5) is between 7 and 8 ----(2)
Step 3 :
Comparing (1) and (2),
(√5 + 6) > (√6 + 5)
8. Answer :
Step 1 :
Approximate (√2 - 1).
√2 is between 1 and 2
(√2 - 1) is between 0 and 1 ----(1)
Step 2 :
Approximate (√10 - 1).
√10 is between 3 and 4
(√10 - 2) is between 1 and 2 ----(2)
Step 3 :
Comparing (1) and (2),
(√2 - 1) < (√10 - 2)
9. Answer :
Step 1 :
Approximate (√2 + 5).
√2 is between 1 and 2
(√2 + 5) is between 6 and 7 ----(1)
Step 2 :
Approximate (√5 + 2).
√5 is between 2 and 3
(√5 + 2) is between 4 and 5 ----(2)
Step 3 :
Comparing (1) and (2),
(√2 + 5) > (√5 + 2)
10. Answer :
Step 1 :
Approximate (√15 - 2).
√15 is between 3 and 4
(√15 - 2) is between 1 and 2 ----(1)
Step 2 :
Approximate (1 + √3).
√3 is between 1 and 2
(1 + √3) is between 2 and 3 ----(2)
Step 3 :
Comparing (1) and (2),
(√15 - 2) < (1 + √3)
11. Answer :
Step 1 :
Using calculator, approximate 𝝅.
𝝅 = 3.1415......
𝝅 is between 3 and 4 ----(1)
Step 2 :
Approximate √2.
√2 is between 1 and 2 ----(2)
Step 3 :
Comparing (1) and (2),
𝝅 > √2
12. Answer :
Step 1 :
Approximate (1 + √3).
√3 is between 1 and 2
(1 + √3) is between 2 and 3 ----(1)
Step 2 :
Approximate (1 + 𝝅).
𝝅 is between 3 and 4
(1 + 𝝅) is between 4 and 5 ----(2)
Step 3 :
Comparing (1) and (2),
(1 + √3) < (1 + 𝝅)
13. Answer :
Step 1 :
Approximate (𝝅 + 2).
𝝅 is between 3 and 4
(𝝅 + 2) is between 5 and 6 ----(1)
Step 2 :
Approximate (e + 2).
e = 2.71828......
e is between 2 and 3
(e + 2) is between 4 and 5 ----(2)
Step 3 :
Comparing (1) and (2),
(𝝅 + 2) > (e + 2)
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