### Squares, cubes and roots

Draw the factor tree as shown in the diagram.
You will get the index notation->729=3*3*3*3*3*3(divide all the numbers by 1000 because we multiplied every number in the question by 1000 to make it easier to calculate)
We can then group the six 3s into three groups of  two 3s->729=(3*3)*(3*3)*(3*3).(all numbers must be divided by 1000)
Since all 3 groups are 3*3, the cube root of 0.729 is 3*3/1000.
The product of 8 and 0.125 is 1.
8=1*8, so 8 is also =8*0.125(to get 1)*8.
Therefore 8= 64*0.125(its the same whether you do 8*8 first or 8*0.125 first)
Hence, 8/0.125=64 and cube root of 64 is 4(refer to factor tree below)because there are again six 2s and can be grouped into 3 groups of two 2s.
64=(2*2)*(2*2)*(2*2).
64
/      \
2      32
/    \
2           16
/     \
2         8
/     \
2             4
/     \
2       2
0.0025=25/10000.(we multiplied the number to make it easier to do the working)
The factor tree of 25 is shown below.
25
/   \
5    5
The two 5s can be grouped into two groups with one 5 in each group->25=(5)*(5)
Hence, the square root of 0.0025 is (5/10000)=0.0005.

1. @Crest: Can't comment now... till after 0000 h which is the deadline for all

2. Feedback on Question 1: Square Root of 0.0025
You are right that the first step is to convert the decimal into a fraction so that you would be dealing with whole numbers only (numerator & denonminator)

You have also clearly described how 25 is factorised; and organising the factors into 2 groups because you are working on square roots.

However, you've forgotten to do the square root for the denominator (10000).

3. Feedback on Question 2: Cube Root of 0.729
Like Question 1, you have clearly explained how you factorised and organised the factors into 3 identical groups.

However, like Question 1, you have forgotten to find the square root of the denominator.

4. Feedback on Question 3:

The following steps
"The product of 8 and 0.125 is 1.
8=1*8, so 8 is also =8*0.125(to get 1)*8.
Therefore 8= 64*0.125(its the same whether you do 8*8 first or 8*0.125 first)"
sounds complicated.

In fact, to do it simply, 8 divided by 0.125 can be expressed as "8 divided by 1/8".
For fractions, we can express it as 8 X 8.
Hence that would result in 64, which could be square rooted.

The rest of the explanation was clear :)

5. SCORE = 8 out of 10 points
Question 1: 2
Question 2: 2
Question 3: 3
Timeliness: 1