What is 85^2 = ?
^ refer to power for e.g. 55 power 2 = ? You have to do this without using calculator.
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Yaa i did the same and solved in just 2 seconds... By the way thanks.But i was knowing it...
Can you add a proof on how it works?
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Haha! ( 1 0 a + 5 ) 2 = 2 5 ( 4 a 2 + 4 a + 1 ) = 1 0 0 a 2 + 1 0 0 a + 2 5 = 1 0 0 a ( a + 1 ) + 2 5 , and this is what he did :D :D
do it totally in mind.
at first, 8 5 × 1 0 0 = 8 5 0 0
then, 8 5 × 1 0 = 8 5 0 + 2 8 5 0 = 1 2 7 5
now, 8 5 0 0 − 1 2 7 5 = 7 2 2 5
I represented 85^2 as (100-15)^2 and then used (a-b)^2=a^2+b^2-2ab to get 85^2=100^2+15^2-2 200 15 =10000+225-3000 =7000+225 =7225
here's a trick maybe some of you might not know
if the one's digits add up to 10 and the ten's digit or hundred, etc e.g. 57 53 or 42 48
what you do is multiply first the one's digits then add one to any of the ten's digit then multiply then just write the product of the ten's digits in front of the one's digits'
example: 42 48, 2 8=16, add 1 to 4 which becomes 5*4=20
42*48=2016
33*37=1221
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To do this, First write 8 then add 1 then multiply with result like 8*(8+1)=72 then square 5, Then result is 7225. This can be used for any number ending with 5.