### Square,Cubes and Roots

Question(1): Find the square root of 0.0025
Solution: 0.0025x 10000 = 25
Prime factors of 25 = 5,5
Square root of 25 = 5
5/10000 = 0.0005
Explanation : We converted the number to whole number so it is easier to use prime factorisation. Then, we find the prime factors of 25 which is 5^2. Next, since we are suppose to find the square root, we grouped it into groups of 2 and the no. is
5 which means 25 = 5x5. Since we now know the square root of 25, we converted it back to decimal form which is 5/10000 = 0.0005.

Question(2): Find the cube root of 0.729.

Solution: 0.729x1000=729

729=3^6

0.729=>0.003^6

Cube root of 0.729 = 0.003^2

= 0.009

Explanation:Since it is harder to use prime factorisation when it is in decimal form, we multiply it by 1000 so it is a whole number.Then, we used the ladder method to find the prime factors of 729 which is 3^6.After that, we converted both numbers to decimals back which is 0.729 and 0.003^6. So, the cube root of 0.729 is 0.003^2 which is 0.009.

Question(3): Find the Cube root of 8/0.125.

Solution: Cube root of 8/0.125 = Cube root of 8 divided by 125/1000

= Cube root of 8 x 1000/125

= Cube root of 8000/125

= Cube root of 64

= 4

Explanation:

Since 8/0.125 is also equal to 8 divided by 125 over 1000, we changed it that form. Then, since 8 divided by 125 over 1000 is also equal to 8 times 1000 over 125 which is 8000 over 125 which is 8000 divided by 125 and the answer is 64. After that, the cube root of 64 is 4 since when we used prime factorisation we will have 2^6. Lastly, we grouped the numbers into groups of 3 and the answer is 4x4x4 which means the cube root of 64 is 4.

1. Feedback on Question 1:

You are right that we need to first convert the decimal into whole number so that it's easier to deal with (we could factorise whole numbers, instead of decimals).

However, why multiply by 10000? What's the reason behind this figure? Why not 1000? 100000? or even 1000000? Could you explain?

The explanation to find the square root of 25 was clear :) Good that you mentioned putting the numbers into 2 groups; however, it's not mentioned into 2 groups of identical factors/ numbers.

1. This comment has been removed by the author.

2. Feedback on Question 2:

Similar to the feedback to Question 1, why multiply by 1000 in order to turn 0.729 into a whole number? Why not 10000 or 100000? Y

ou would have to look at the decimal as a whole - Express it as a fraction so that you could deal with the numerator and the denominator separately. Both numerator and denominator are whole numbers, and therefore we could factorise it.

On another note: while 729 = 3^6
Does it mean that 0.729 same as 0.003^6?
Work out 0.003^6 to check it out.

3. Question 3 is well answered :)

4. SCORE = 4 out of 10 pts
Question 1: 1
Question 2: 0
Question 3: 3
Timeliness: 0