5. a) Which of these numbers are perfect squares? Why?

i) 1 ii) 24 iii) 225 iv) 500

b) Use the factor rainbow to determine if

289 is a perfect square. Explain your

reasoning.
PLZ HELP

Part A: 1 & 225, A number times itself equals a perfect Square.

Part B: No, 289 is NOT perfect square.

Step-by-step explanation:

Part A: 1*1=1, 15*15=225 (Perfect Squares)

Part B: Utilizing the Factor Rainbow one can see that the same number does not exist on both sides of the rainbow simultaneously.

Answer and Eplainations:

i) 1 is a perfect square because 1 x 1  = 1

ii) 24 is not a perfect square because it is a natural number. Natural numbers cannot be squared.

iii) 225 is a perfect square 15 x 15 = 225

iv) 500 is not a perfect square it is an irrational number

289 is a perfect square because 17 x 17 = 289

the square root of 289 is 17 therefore it is a perfect square

A Tip that will help you with other problems like this any nunmber ending in 2, 3, 7, or 8 can never be a perfect square.

Hope this helps! Good luck!

24

step-by-step explanation:

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)