Question

Any1 can help me wif q12

Answer 1

I) HCF - use the smallest powers of each common factors
HCF (A,B) = 2^2 × 3^4 × 5^2

LCM - use the highest powers of each factors
LCM (A,B) = 2^4 × 3^6 × 5^2 × 7^2 × 11^16

ii) Add powers together.
A×B = 2^6 × 3^10 × 5^4 × 7^2 × 11^16
sqrt(A × B)
Divide powers by 2.
sqrt(A × B) = 2^3 × 3^5 × 5^2 × 7 × 11^8

iii) C = 3^7 × 5^2 × 7
Ck = (3^7 × 5^2 × 7) × k
B/c Ck should be a product that is a perfect cube, the powers of the products should be divisible by 3.
(3^7 × 5^2 × 7) × k = 3^9 × 5^3 × 7^3

k = (3^9 × 5^3 × 7^3) / (3^7 × 5^2 × 7)
k = 3^(9-7) × 5^(3-2) × 7^(3-1)
k = 3^2 × 5 × 7^2