Which of the following numbers have the digit 6 in the units place? (i) 38² (ii) 34² (iii) 46² (iv) 56² (v) 74² (vi) 82²
Rule: Numbers ending with 4 or 6 have squares ending with 6.
(i) 38²: 38² = 1444 Ends with 4
(ii) 34²: 34² = 1156 Ends with 6 ✓
(iii) 46²: 46² = 2116 Ends with 6 ✓
(iv) 56²: 56² = 3136 Ends with 6 ✓
(v) 74²: 74² = 5476 Ends with 6 ✓
(vi) 82²: 82² = 6724 Ends with 4
Answer: The squares ending with digit 6 are: 34² = 1156, 46² = 2116, 56² = 3136, and 74² = 5476.
Explanation
The chapter explains that if a number has 4 or 6 in the units place, its square ends with 6. Numbers 34, 46, 56, and 74 end with 4 or 6, so their squares end with 6. Numbers 38 and 82 end with 8 and 2 respectively, so their squares end with 4.
Solution Steps
Step 1: Calculate 38² = 1444 (ends with 4)
Step 2: Calculate 34² = 1156 (ends with 6)
Step 3: Calculate 46² = 2116 (ends with 6)
Step 4: Calculate 56² = 3136 (ends with 6)
Step 5: Calculate 74² = 5476 (ends with 6)
Step 6: Calculate 82² = 6724 (ends with 4)