Question

10

(i)
(ii)
Express 17 150 as a product of its prime factors in index notation.
[1]
Find the smallest integer n, such that 17 150n is a perfect square.
[1]
5x17150
It is given that
is a prime number. State all possible integer values of x.
(iii)
CTX 120167

Answer 1

`ii)\\a) 17150=2*5^2*7^3\\b) 17150*n=k^2 ==> n=2*7=14\\\\iii)\\\sqrt[3]{(5*2*5^2*7^3)/(n) } =7*5*\sqrt[3]{(2)/(n) } \\\\1)\ n=2*5^3=250\\2)\ n=2*7^3=686\\`