Can you solve this easy problem?

Algebra Level 1

What is 85^2 = ?

^ refer to power for e.g. 55 power 2 = ? You have to do this without using calculator.


The answer is 7225.

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4 solutions

Dupleshwar Yadav
Aug 6, 2015

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.

Yaa i did the same and solved in just 2 seconds... By the way thanks.But i was knowing it...

Shubham Joshi - 5 years, 10 months ago

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Yes I did the same too

Ahmad fikri Azhari - 2 years, 8 months ago

Can you add a proof on how it works?

Pranjal Jain - 5 years, 10 months ago

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Haha! ( 10 a + 5 ) 2 = 25 ( 4 a 2 + 4 a + 1 ) = 100 a 2 + 100 a + 25 = 100 a ( a + 1 ) + 25 (10a + 5)^2 = 25(4a^2 + 4a + 1) = 100a^2 + 100a + 25 = 100a(a + 1) + 25 , and this is what he did :D :D

Satyajit Mohanty - 5 years, 10 months ago

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Looks good! ¨ \ddot\smile

Pranjal Jain - 5 years, 10 months ago
Mohammad Khaza
Apr 1, 2018

do it totally in mind.

at first, 85 × 100 = 8500 85 \times 100=8500

then, 85 × 10 = 850 + 850 2 = 1275 85 \times 10=850+\frac{850}{2}=1275

now, 8500 1275 = 7225 8500-1275=7225

Smiti Mittal
Sep 19, 2015

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

Caeo Tan
Aug 17, 2015

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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