The product of the squares of two positive integers is 400. How many pairs of positive integers satisfy this condition? A. 0 B. 1 C. 2 D. 3 E.4

(D) 400 = 2 × 2 × 2 × 2 × 5 × 5 Combine the prime factors in pairs.

400 = (2 × 2) × (2 × 2) × (5 × 5) Now brake the factorization into two parts, each one will be a square. The possible combinations are: 400 = (2 × 2) × [(2 × 2) × (5 × 5)] 400 = [(2 × 2) × (2 × 2)] × (5 × 5) But don't forget that 400 = 1 × 400, where 1 = 1². So we also have: 400 = (1 × 1) × [(2 × 2) × (2 × 2) × (5 × 5)]

Thus all the possible combinations of the factors that make the product of two squares are the following: 1² × 20² = 400 2² × 10² = 400 4² × 5² = 400

There are three possible pairs that fit the criterion. The correct answer is D. --------- The answer should be E. 4 , because your explanation has missed the possibility of 20² × 20² . It is not mentioned that the numbers should be distinct.

The answer should be E. 4 , because your explanation has missed the possibility of 20² × 20² . It is not mentioned that the numbers should be distinct.

Users browsing this forum: No registered users and 4 guests

You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot post attachments in this forum