COMPARING IRRATIONAL NUMBERS WORKSHEET

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.

Answers

1. Answer :

Step 1 :

Square 5√3.

(5√3)² = 5²(√3)²

= 25(3)

= 75 ----(1)

Step 2 :

Square 7√2.

(7√2)² = 7²(√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 = 4²(√5)²

= 16(5)

= 80 ----(1)

Step 2 :

Square 3√10.

(3√10)² = 3²(√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 = 2²(√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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