Question

(1). Find the smallest number on dividing by which 9408 becomes a perfect square, also find the square root
of the number obtained by prime factorization method.
(2). Using prime factorization, find the smallest number, on multiplying by which, 1536 will yield a perfect
square, also find the square root of the perfect square their obtained.
(3). Write the Pythagorean triplets with the following numbers as one of its members (a) 24
(b) 45​

Answer 1

Step-by-step explanation:

1) 9408

9,408 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 3

divide 9408 by 3 to get a perfect square

9408 ÷ 3 = 3136

3136 is a perfect square of 56

2) 1536

1,536 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3

multiply 1536 with 6 to get a perfect square

1536 × 6 = 9216

9216 is a perfect square of 96

3)

a) 24

the Pythagorean triplet is (24, 7, 25)

${25}^{2} = {24}^{2} + {7}^{2} \\ 625 = 576 + 49 \\ 625 = 625$

b) 45

the Pythagorean triplet is (45, 28, 53)

${53}^{2} = {45}^{2} + {28}^{2} \\ 2809 = 2025 + 784 \\ 2809 = 2809$

hope you get your answer