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We know that we can express any 2 digit number as 10m+n , where m is the digit at tens place and n is the digit at ones place.

∴ the number ending with 3 can be expressed as 10m+3.

(10m + 3)² = (10m)² + 2×10m×3 + 3² …………using, (x+y)² = x² + 2xy + y²

= 100m² + 10× 6m + 9

Clearly, we can observe that the square ends in 9.

The number ending with 5 can be expressed as 10m+5.

(10m + 5)² = (10m)² + 2×10m×5 + 5² …………using, (x+y)² = x² + 2xy + y²

= 100m² + 100m + (25)

= 100 (m² + m) + (10×2 + 5 )

Clearly, we can observe that the square ends in 5.

The number ending with 4 can be expressed as 10m+4.

(10m + 4)² = (10m)² + 2×10m×4 + 4² …………using, (x+y)² = x² + 2xy + y²

= 100m² + 10× 8m + (16)

= 100m² + 10× 8m + (10 + 6)

= 100 m² + 10× (8m+1) + 6

Clearly, we can observe that the square ends in 6.