Squaring of a number ending in 5

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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 writtenin expanded form: n10 + 5

For 85, n=8: 810+5

Graphical Approach:

A square of a length ending in 5: n10+5

5

5

n10

n10

Graphical Approach:

55

n10

n10

A square of a length ending in 5: n10+5

Graphical Approach:

5 5

n10

n10

25

A square of a length ending in 5: n10+5

Graphical Approach:

5 5

n10

n10 25

A square of a length ending in 5: n10+5

Graphical Approach:

A square of length ending in 5: n10+55 5

n10

n10 25

(n10)(n10)

5(n10)

5(n10)

Graphical Approach:

5 5

n10

n10 25

(n10)(n10)

5(n10)

5(n10)

A square of length ending in 5: n10+5

Graphical Approach:

5 5

n10 25

(n10)[(n10)+5+5]

n10

Area:

(n10)(n10)

5(n10)

5(n10)

A square of length ending in 5: n10+5

Graphical Approach:

10

n10

n10 25

(n10)[(n10)+10] = (n10)[(n+1)10]

Area:

A square of length ending in 5: n10+5

Graphical Approach:

10

n10

n10(n10)[(n10)+10] = (n10)[(n+1)10]

Area:

+ 25 + 25

A square of length ending in 5: n10+5

Graphical Approach:

10

n10

n10

Area: (n)(n+1)1010+25

25

Graphical Approach:

Area: (n)(n+1)1010+2510

n10

n10 25

Graphical Approach:

Area: (n)(n+1)1010+2510

n10

n10 25

= n(n+1) 25

100’s 10’s &1’s

Graphical Approach:

10

n10

n10 25

For 85, n=8

= n(n+1) 25

100’s 10’s &1’s

8585 =

= n(n+1) 25

100’s 10’s &1’s

8585 =

Graphical Approach:

10

n10

n10 25

For 85, n=8

8585 =

89 25 7 2 25

= n(n+1) 25

100’s 10’s &1’s

8585 =

Graphical Approach:

10

n10

n10 25

For 85, n=8

8585 = 7225

Examples

2525 = 6 25

3535 = 12 25

5555 = 30 25

(n10+5)(n10+5) = n(n+1) 25 100’s

115115 =

495495 =

995995 =

132 25

2450 25

9900 25