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Squaring of a number ending in 5

Squaring of a number ending in 5. An approach to determine answers Quickly!. Squaring of a number ending in 5. Squaring of a number ending in 5. 85 = 80 + 5. Generalization: n is any number (e.g., 1, 2, 3 , … ). Any number ending in 5 can be written in expanded form: n  10 + 5.

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Squaring of a number ending in 5

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  1. Squaring of anumber ending in 5 An approach to determine answers Quickly! Squaring of anumber ending in 5

  2. Squaring of anumber ending in 5 85 = 80 + 5 Generalization: n is any number (e.g., 1, 2, 3, …) Any number ending in 5 can be written in expanded form: n10 + 5 For 85, n=8: 810+5

  3. n10 5 n10 5 Graphical Approach: A square of a length ending in 5: n10+5

  4. n10 n10 5 5 Graphical Approach: A square of a length ending in 5: n10+5

  5. n10 25 n10 5 5 Graphical Approach: A square of a length ending in 5: n10+5

  6. 25 Graphical Approach: A square of a length ending in 5: n10+5 5 5 n10 n10

  7. 25 Graphical Approach: A square of length ending in 5: n10+5 5 5 n10 5(n10) (n10) (n10) n10 5(n10)

  8. 5(n10) (n10) (n10) 25 5(n10) Graphical Approach: A square of length ending in 5: n10+5 5 5 n10 n10

  9. 5(n10) (n10) (n10) 25 5(n10) Graphical Approach: A square of length ending in 5: n10+5 5 5 n10 Area: n10 (n10)[(n10)+5+5]

  10. 25 Graphical Approach: A square of length ending in 5: n10+5 10 n10 Area: n10 (n10)[(n10)+10] = (n10)[(n+1)10]

  11. Graphical Approach: A square of length ending in 5: n10+5 10 n10 Area: n10 (n10)[(n10)+10] = (n10)[(n+1)10] + 25 + 25

  12. 25 Graphical Approach: Area: (n)(n+1)1010+25 10 n10 n10

  13. 10 n10 25 n10 Graphical Approach: Area: (n)(n+1)1010+25

  14. 10 n10 25 n10 Graphical Approach: Area: (n)(n+1)1010+25 = n(n+1) 25 100’s 10’s &1’s

  15. 10 8585 = n10 = n(n+1) 25 100’s 10’s &1’s 25 n10 Graphical Approach: For 85, n=8

  16. 10 8585 = n10 = n(n+1) 25 100’s 10’s &1’s 25 n10 Graphical Approach: For 85, n=8 8585 = 89 25 7 225

  17. 10 8585 = n10 = n(n+1) 25 100’s 10’s &1’s 25 n10 Graphical Approach: For 85, n=8 8585 = 7225

  18. Examples (n10+5)(n10+5) = n(n+1)25 100’s 2525 = 132 25 6 25 115115 = 3535 = 12 25 495495 = 2450 25 5555 = 30 25 995995 = 9900 25

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