**Comparing irrational numbers worksheet :**

Worksheet on comparing irrational numbers is much useful to the students who would like to practice problems on irrational numbers.

1. Compare ** (****√3 + 5) and (3 + ****√5) and write <, >, or = in between them. **

**2. **Compare ** (****√2 + 4) and (2 + ****√4) and write <, >, or = in between them. **

**3. **Compare ** 4****√2 and 3****√3 and write <, >, or = in between them. **

**4. **Compare ** (****√12 + 6) and (12 + ****√6) and write <, >, or = in between them. **

**5. **Compare ** (****√5 + 6) and (5 + ****√6) and write <, >, or = in between them. **

**6. **Compare ** (****√3 + 3) and (****√3**** + ****√9) and write <, >, or = in between them. **

**Question 1 : **

Compare ** (****√3 + 5) and (3 + ****√5) and write <, >, or = in between them. **

**Answer : **

**Step 1 : **

First approximate **√3. **

**√3 is between 1 and 2 **

**Next approximate ****√5. **

**√5 is between 2 and 3. **

**Step 2 :**

Then use your approximations to simplify the expressions.

**√3 + 5 is between 6 and 7. **

**3 + √5 is between 5 and 6. **

**So, √3 + 5 > 3 + ****√5****. **

**Question 2 : **

Compare ** (****√2 + 4) and (2 + ****√4) and write <, >, or = in between them. **

**Answer : **

**Step 1 :**

First approximate **√2. **

**√2 is between 1 and 2 **

**Next approximate ****√4. **

**√4 is equal 2. **

**Step 2 :**

Then use your approximations to simplify the expressions.

**√2 + 4 is between 5 and 6. **

**2 + √4 is equal to 4. **

**So, √2 + 4 > 2 + ****√4****. **

**Question 3 : **

Compare ** 4****√2 and 3****√3 and write <, >, or = in between them. **

**Answer : **

**Key concept : **

Square both irrational numbers and compare them.

**Step 1 :**

Take square to the number 4**√2. **

**(4√2)**² = (4)²(**√2)**²

**(4√2)**² = (16)(**2)**

**(4√2)**² = 32 --------> (1)

**Step 2 :**

Take square to the number 3**√3. **

**(3√3)**² = (3)²(**√3)**²

**(3√3)**² = (9)(**3)**

**(3√3)**² = 27 --------> (2)

**Step 3 :**

From (1) and (2), we get

32 > 27 -----> **4√2 > ****3√3**

**Question 4 : **

Compare ** (****√12 + 6) and (12 + ****√6) and write <, >, or = in between them. **

**Answer : **

**Step 1 :**

First approximate **√12. **

**√12 is between 3 and 4 **

**Next approximate ****√6. **

**√6 is between 2 and 3. **

**Step 2 :**

Then use your approximations to simplify the expressions.

**√12 + 6 is between 9 and 10. **

**12 + √6 is between 12 and 14. **

**So, √12 + 6 < 12 + ****√6****. **

**Question 5 : **

Compare ** (****√5 + 6) and (5 + ****√6) and write <, >, or = in between them. **

**Answer : **

**Step 1 :**

First approximate **√5. **

**√5 is between 2 and 3 **

**Next approximate ****√6. **

**√6 is between 2 and 3. **

**Step 2 :**

Then use your approximations to simplify the expressions.

**√5 + 6 is between 8 and 9. **

**5 + √6 is between 7 and 8. **

**So, √5 + 6 > 5 + ****√6****. **

**Question 6 : **

Compare ** (****√3 + 3) and (****√3**** + ****√9) and write <, >, or = in between them. **

**Answer : **

**Step 1 :**

**√3 + 3 --------> (1)**** **

**Step 2 :**

**Find the value of ****√9. **

**√9 is equal to 3. **

**Step 3 :**

**√3 + ****√9 = ****√3 + 3 ****--------> (2)**** **

**Step 4 :**

**From (1) and (2), we get**

**√3 + 3**** = ****√3 + ****√9**

After having gone through the stuff given above, we hope that the students would have understood "Comparing irrational numbers worksheet".

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