Math, asked by harishsinghmanan, 3 days ago

Using prime factorization, check if the following numbers are perfect squares.
a. 784 b. 1254 c. 2116 d. 10093 ​

Answers

Answered by UrAnswerbook
1

Answer:

Answer:

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.

Step-by-step explanation:

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