Scribe 6 Questions 24 and 27

Question 24:

A) What are the next three triangular numbers?

-The next three triangular numbers are 10, 15 and 21. In the first triangle pattern, the number of triangles was 1. The second pattern the number of triangles was 3. It went up by 2. The next triangle pattern had 6 triangles in it, and it went up by 3 from the last pattern. I could only assume that the number of triangles went up one more than what it did last time, so 6+4=10. Then, 10+5=15, and so on.

B) Add together any two consecutive triangle numbers. What do you notice about the sums?

-They are all perfect squares. Example: 3+6=9. The square root of 9 is 3. 1+3=4. The square root of 4 is 2.

Question 27:

A) Determine the square root of each number:

-Square root of 6400=80. Square root of 640 000=800. Square root of 64 000 000=8000.

B) Describe a quick method for determining mentally the square root of each number in part a).

-If the square root of 6400=80, 640 000 has 2 more 0's than 6400. So you add another 0 to the square root answer. For 64 000 000, add another 0. Basically, add one more 0 to the square root for ever 2 0's in the number.

C) Explain why this method does not work for evaluating the square root of 640

-It doesn't work because 640 is not a perfect square.

D) Use your method in part b) to evaluate the square root of 640 000 000 000. Explain how you determined the answer.

-640 000 000 000 has 10 0's. 10/2=5. So, the square root of 640 000 000 000 is 8 with 5 0's, or 800000.