Sure!

While thinking about 37^3 I came across an interesting way of doing this, making the calculation easier (I hope).

First, let’s square 37 using (40-3)^2:

37 * 37 = 34 * 40 + 9 = 1,369

Now 1,369 is almost 1,370.

Let’s do 3 times 1,370 first.

Forget about the last zero for now and do 3 x 137.

3 x 13 = 39 and 3 x7 = 21, so the multiplication gives:

39 | 21

Take care of the carry to get:

411

If 3 x 137 = 411, then 3 x 1370 = 4,110. Done.

(as always, a lot of work to write out; goes quick in your mind)

Alternatively do:

3 x 1,300 = 3,900

3 x 70 = 210.

add 210 to 3,900 to get 4,110.

Now this is 3 X1,370. We need 3 X 1,369, so subtract 3 to get 4,107.

Next step: 7 X 1,369.

We could multiply 7 times 1,369, but what if I told you a quick subtraction is enough?

Because 7 =10 -3, we can do:

7 X 1,360 = (10-3) * 1369 =

13,690 - 3 X 1,369 =

13,690 - 4,107 (Remember we just calculated 3 * 1,369 = 4,107, so no need to do that again)

In your mind, just add a zero to 1369 and subtract the number you just calculated doing 3 times 1369 (4,107).

13,690

4,107 -

_ _

9,583

If 3 times 1369 = 4107, then 30 times 1369 = 41,070

Now add 7 times 1369 = 9,583

41,070

9,583 +

_ _

50,653

It takes some time to write this out and maybe it takes some time for you to do this mentally,

**but how many of your friends can do 37^3 mentally?**