Use a calculator to compute the following....

Compute the following :

15^2

25^2

35^2

45^2

55^2

 

Desceibe a shortcut you could use to get the above answers mentally. Show that your shortcut works for larger numbers ending in 5 and explain why.

Expert Answers

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We have to be careful when approaching this mentally. One idea may jump to one mind is to think 15=10+5 so 10^2+5^2=... That would be incorrect because (a+b)^2 is not equal to a^2+b^2.

The way I will aproach this problem is by thinking about the double of the original. Square it, then divide by 4. To divide by 4, you will half twice. So for example

`(15)^2=(30/2)^2=30^2/(2^2)=30^2/4=900/4=450/2=225`

Similar

`(35)^2=70^2/4=4900/4=2450/2=1225`

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