Question

Explain how you can solve 8x8 if you know how to multiply with 4 but not how to multiply with 8

Answer 1

Turn the 8's into 4's and 2's:

8×8
4×2×4×2
4×4×4
16×4
64

Or just turn one of the 8's into 4 and 2
8×8
8×4×2
16×4 or 32×2
64

Answer 2

If you only know how to multiply with 4's, then you need to quickly convert the 8's to 4's.

We were given,

$8\times8$

So we rewrite each of the 8's as

$(4\times2)\times(4\times2)$

Perfectly for us,it turns out that the 2's will also give us a 4, so the whole thing becomes,

$4\times4\times2\times2=4\times4\times4$

$\Rightarrow 8\times8=4\times4\times4$

Now, let us multiply two of the 4's, to obtain,

$\Rightarrow 8\times8=16\times4$

Finally, let us multiply with the last 4 to get,

$\Rightarrow 8\times8=64$