how do i explain to my child how to solve l Squared = 1296 is the same as l=36

Question

other than trial and error - how do you solve for l from that point?

Answer 1

Break down the 1296 into smaller SQRT's.

The SQRT 1296 = (SQRT 4) (SQRT 324) = (SQRT 4)(SQRT 4)(SQRT 81) = (2)(2)(9) =36

Answer 2

Taking the square root isn't a simple operation like taking the square is. So we can't just so this directly. We have to get some clues and go from there.

So, we need a number that, when it gets multiplied by itself, gives me a number that ends in 6. What could the two numbers be?

1*1 = 1.

2*2 = 4

3*3 = 9

4*4 = 16 (this one ends in a 6)

5*5 = 25

6*6 = 36 (this one also ends in a 6)

7*7 = 49

8*8 = 64

9*9 = 81.

So we know that our number has to end in a 4 or a 6. So, 4, 6, 14, 16, 24, 26, etc. are numbers that might work. Let's look at squares of the multiples of 10 now.

10*10 = 100 (smaller than 1296)

20*20 = 400 (smaller than 1296)

30*30 = 900 (smaller than 1296)

40*40 = 1600 (bigger than 1296)

So we know our number has to be between 30 and 40.

Also 1296 is divisible by 3 (because 1+2+9+6 = 18, which is divisible by 3, and that's the divisibility rule for 3)

So we need a number between 30 and 40 that ends in 4 or 6 AND is a multiple of 3.

36 is our only choice. We then verify: 36*36 = 1296.