Yuctoborian : A math shortcut for squaring numbers that end in 5
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Transcript of Yuctoborian : A math shortcut for squaring numbers that end in 5
![Page 1: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/1.jpg)
Squares of halves
![Page 2: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/2.jpg)
1.52 = ( 1 x 2 ) + 0.25 = 2.25
2.52 = ( 2 x 3 ) + 0.25 = 6.25
3.52 = ( 3 x 4 ) + 0.25 = 12.25
4.52 = ( 4 x 5 ) + 0.25 = 20.25
![Page 3: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/3.jpg)
1.52 = ( 1 x 2 ) + 0.25 = 2.25
2.52 = ( 2 x 3 ) + 0.25 = 6.25
3.52 = ( 3 x 4 ) + 0.25 = 12.25
4.52 = ( 4 x 5 ) + 0.25 = 20.25
![Page 4: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/4.jpg)
1.52 = ( 1 x 2 ) + 0.25 = 2.25
2.52 = ( 2 x 3 ) + 0.25 = 6.25
3.52 = ( 3 x 4 ) + 0.25 = 12.25
4.52 = ( 4 x 5 ) + 0.25 = 20.25
![Page 5: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/5.jpg)
1.52 = ( 1 x 2 ) + 0.25 = 2.25
2.52 = ( 2 x 3 ) + 0.25 = 6.25
3.52 = ( 3 x 4 ) + 0.25 = 12.25
4.52 = ( 4 x 5 ) + 0.25 = 20.25
![Page 6: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/6.jpg)
1.52 = ( 1 x 2 ) + 0.25 = 2.25
2.52 = ( 2 x 3 ) + 0.25 = 6.25
3.52 = ( 3 x 4 ) + 0.25 = 12.25
4.52 = ( 4 x 5 ) + 0.25 = 20.25
In other words, multiply the whole numbers above and below the half, then add 0.25.
![Page 7: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/7.jpg)
1.52 = ( 1 x 2 ) + 0.25 = 2.25
2.52 = ( 2 x 3 ) + 0.25 = 6.25
3.52 = ( 3 x 4 ) + 0.25 = 12.25
4.52 = ( 4 x 5 ) + 0.25 = 20.25
In other words,
multiply the whole numbers above and below the half,
![Page 8: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/8.jpg)
1.52 = ( 1 x 2 ) + 0.25 = 2.25
2.52 = ( 2 x 3 ) + 0.25 = 6.25
3.52 = ( 3 x 4 ) + 0.25 = 12.25
4.52 = ( 4 x 5 ) + 0.25 = 20.25
In other words,
multiply the whole numbers above and below the half,
Then add 0.25
![Page 9: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/9.jpg)
Squares of whole numbers ending in 5
![Page 10: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/10.jpg)
152 = 1x2 then attach 25 = 225
252 = 2 x 3 then attach 25 = 625
752 = 7 x 8 then attach 25 = 5625
8052 = 80 x 81 then attach 25 = 648025
![Page 11: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/11.jpg)
152 = 1x2 then attach 25 = 225
252 = 2 x 3 then attach 25 = 625
752 = 7 x 8 then attach 25 = 5625
8052 = 80 x 81 then attach 25 = 648025
![Page 12: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/12.jpg)
152 = 1x2 then attach 25 = 225
252 = 2 x 3 then attach 25 = 625
752 = 7 x 8 then attach 25 = 5625
8052 = 80 x 81 then attach 25 = 648025
![Page 13: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/13.jpg)
152 = 1x2 then attach 25 = 225
252 = 2 x 3 then attach 25 = 625
752 = 7 x 8 then attach 25 = 5625
8052 = 80 x 81 then attach 25 = 648025
![Page 14: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/14.jpg)
Squares of decimal numbers ending in 5
![Page 15: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/15.jpg)
0.752 = 7 x 8, then attach 25 = 5625
![Page 16: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/16.jpg)
0.752 = 7 x 8, then attach 25 = 5625
(But where does the decimal point go?)
![Page 17: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/17.jpg)
0.752 = 7 x 8, then attach 25 = 5625
(But where does the decimal point go?)
![Page 18: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/18.jpg)
The number is ‘three-quarters of three-quarters.’
That has to be close to ½.
0.752 = 7 x 8, then attach 25 = 5625
(But where does the decimal point go?)
![Page 19: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/19.jpg)
The number is ‘three-quarters of three-quarters.’
That has to be close to ½.
(But where does the decimal point go?)
0.752 = 7 x 8, then attach 25 = 0.5625
![Page 20: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/20.jpg)
1.052 = 10 x 11 then attach 25 = 11025
0.752 = 7 x 8, then attach 25 = 0.5625
![Page 21: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/21.jpg)
1.052 = 10 x 11 then attach 25 = 11025
The answer has to be slightly larger than 1.
0.752 = 7 x 8, then attach 25 = 0.5625
![Page 22: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/22.jpg)
1.052 = 10 x 11 then attach 25 = 1.1025
0.752 = 7 x 8, then attach 25 = 0.5625
![Page 23: Yuctoborian : A math shortcut for squaring numbers that end in 5](https://reader036.fdocuments.us/reader036/viewer/2022062300/55556f4bb4c9058a5a8b49d5/html5/thumbnails/23.jpg)
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