I chose numbers 24 and 27.
24. The first three triangular numbers are 1, 3, and 6.
A) What are the next three triangular numbers?
B) Add together any two consecutive
triangular numbers. What do you notice about the sums?
A) 10, 15, 21.
B) The sums are all perfect squares.
27. A) Determine the square root of each number: 6400, 640 000,64 000 000.
B) Describe a quick method for determining mentally the square root of each numbe in part a).
C) Explain why this method does notwork for evaluating √640.
D)Use your method in part b) to evaluate √640 000 000 000 . Explain how you determine
27. A) √6400=80
B) First, ignore all the zero. Have you noticed that 64 is always there? If so, that means 8 is our first digit for each on of the square root. Why?Because the square root of 64 is 8. Next, pair all the zeros into 2. A pair of zero represents a zero after the 8. That means if there is 3 pairs of zero, then there will be 3 zeros after the eight.
C) The method I used can only work if all zeros have a partner.
D) First I ignore all the zero. I was left with 64.Since I know that the square root of 64 is 8. Then I already know that the first digit of my square root is 8. Next, I paired all the zero. I ended up with 5 pairs. Since I know that there are 5 pairs all I have to do is put them after 8. After all
those steps my answer is 80,000.
How to find a square root without calculator