is 129 is perfect cube we are using prime factorization methode to check
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hey mate ,here is your answer
Step-by-step explanation:
→ The perfect squares are : 400, 1296, 9025
→ Step-by-step explanation:
→ For a number to be a perfect square it's prime factors should be to a power of 2, or any even number.
→ We will write the prime factors of each of the numbers as follows :
→ 400 = 2 × 2 × 2 × 2× 5 × 5 = 2⁴ × 5²
→ The prime factors have even powers hence 400 is a perfect square.
→ 768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3
→ 2^8 × 3
→ One of the prime factors (3) has an odd power hence 768 is not a perfect square.
→ 1296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3
→ 2⁴ × 3⁴
→ Since the powers of the prime factors are even then 1296 is a perfect square.
→ 8000 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5 = 2^6 × 5³
→ Since one of its prime factors has an odd power then 8000 is not a perfect square.
→ 9025 = 5 × 5 × 19 × 19 = 5² × 19²
→ Since both prime factors have an even power then 9025 is a perfect square.
hope you have been understood.
thank you be happy forever
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