Question

1. Using the prime factorization method, find which of the following numbers are perfect
squares:
(i) 225
(ii) 189
(iii) 441
(iv) 729
(v) 1575
(iv) 900​

Answer 1

Answer:

i,ii,iv,vi

Step-by-step explanation:

keep fine and good

Answer 2

Answer:

(i) ✔

(ii) ❌

(iii) ✔

(iv) ✔

(v) ❌

(iv) ✔

Step-by-step explanation:

(i) 225 = 3 × 3 × 5 × 5 = 3² × 5² = 15²

this is a perfect square

(ii) 189 = 3 × 3 × 3 × 7 = 3³ × 7

this is not a perfect square

(iii) 441 = 3 × 3 × 7 × 7 = 3² × 7² = 21²

this is a perfect square

(iv) 729 = 3 × 3 × 3 × 3 × 3 × 3 = 3³ × 3³ = 27 × 27 = 27²

this is a perfect square

(v) 1575 = 3 × 3 × 5 × 5 × 7 = 3² × 5² × 7 = 15² × 7

this is not a perfect square

(iv) 900​ = 2 × 2 × 3 × 3 × 5 × 5 = 2² × 3² × 5² = 30²

this is a perfect square