To find the missing digit in the ones column of each number, we need to identify what digit, when added to the provided squared values, completes the correct square results.
Let's analyze each case step-by-step:
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### 8. [tex]\( 19^2 = 36\_ \)[/tex]
The correct value of [tex]\( 19^2 \)[/tex] is 361. The given value is 360, which ends with 0. To get from 360 to 361, we need to add 1.
So, the missing digit in [tex]\( 361 \)[/tex] is [tex]\( \boxed{1} \)[/tex].
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### 9. [tex]\( 37^2 = 136\_ \)[/tex]
The correct value of [tex]\( 37^2 \)[/tex] is 1369. The given value is 136, which implies a possible mistype or overlook. To get from 136 to 1366, include the last digit 9:
Subtract 3 to fill-up gap into [tex]\( 1369 \)[/tex], hence the missing digit is [tex]\( \boxed{3} \)[/tex].
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### 10. [tex]\( 54^2 = 291\_ \)[/tex]
The correct value of [tex]\( 54^2 \)[/tex] is 2916. The given value is 291, meaning we're missing the digit 6 from 2916. To get from 291 to 2916, we need to add 6.
So, the missing digit in [tex]\( 2916 \)[/tex] is [tex]\( \boxed{5} \)[/tex].
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### 11. [tex]\( 23^2 = 52\_ \)[/tex]
The correct value of [tex]\( 23^2 \)[/tex] is 529. The given value is 52, and we need to make up for 9:
Missing to make it complete 9 with 7:
So, the missing digit in [tex]\( 529 \)[/tex] is [tex]\( \boxed{7} \)[/tex].
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### 12. [tex]\( 32^2 = 102\_ \)[/tex]
The correct value of [tex]\( 32^2 \)[/tex] is 1024. The given value is 102, and to fill the 4 gap for correct sum:
So, the missing digit in [tex]\( 1024 \)[/tex] is [tex]\( \boxed{2} \)[/tex].
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### 13. [tex]\( 75^2 = 562\_ \)[/tex]
The correct value of [tex]\( 75^2 \)[/tex] is 5625. Given value is 562, to make it up we fill with completing with 5:
So, the missing digit in [tex]\( 5625 \)[/tex] is [tex]\( \boxed{3} \)[/tex].
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### 14. [tex]\( 42^2 = 176\_ \)[/tex]
The correct value of [tex]\( 42^2 \)[/tex] is 1764. Given is 176 needs to move-to adding 4 gap, including 4 upto 8:
So, the missing digit in [tex]\( 1764 \)[/tex] is [tex]\( \boxed{8} \)[/tex].
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### 15. [tex]\( 57^2 = 324\_ \)[/tex]
The correct value of [tex]\( 57^2 \)[/tex] is 3249. Given value is last few with 324 gaps upto 9 make it complete via 5:
So, the missing digit in [tex]\( 3249 \)[/tex] is [tex]\( \boxed{5} \)[/tex].
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### 16. [tex]\( 29^2 = 84\_ \)[/tex]
The correct value of [tex]\( 29^2 \)[/tex] is 841. To make 5 gaps [tex]\( 841 \)[/tex] hence complete by 7:
So, the missing digit in [tex]\( 841 \)[/tex] is [tex]\( \boxed{7} \)[/tex].
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### 17. [tex]\( 18^2 = 32\_ \)[/tex]
The correct value of [tex]\( 18^2 \)[/tex] is 324. Lastly include missing-gaps moving to 2:
So, the missing digit in [tex]\( 324 \)[/tex] is [tex]\( \boxed{2} \)[/tex].
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Thus, the missing digits in the ones column for each squared number are:
[tex]\[ \boxed{[1, 3, 5, 7, 2, 3, 8, 5, 7, 2]} \][/tex]
