Can you stop checking for factor pairs when you find a pair that repeats? explain

Solution:

Consider numbers which are Squares,cubes, fourths, fifths of some natural numbers.

For example, Starting from squares of some natural number: 4,9,16,25,36,49,64

and their factors , which are 4= 1 × 2×1×2

9=1×3×1×3

16=2×1×2×1×2×1×2×1

25=1×5×1×5

36=2×3×2×3

64=2×4×2×4

Now coming to cubic numbers

8= 1 ×2×1×2×1×2

27= 1×3×1×3×1×3

3125= 3 ×5×3×5×3×5

So,the numbers whose factor pairs repeats are square, cubic, fourth,Fifth ,Sixth andhigher powers of natural Numbers.

→→→So, we just need to check that whether those numbers whose factor pairs repeats are Squares, cubes or higher powers of natural numbers.

rotated. i took the test

step-by-step explanation:

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584