Question

Check out which of the following numbers are perfect squares using prime factorization 256,169,226,100,121,299,324,1024,2027,10404

Answer 1

Answer:

every point is of each number hope this will help you

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step-by-step explanation:

• 1Adding one we get (8 + 1) = 9. Therefore 256 has 9 factors. 256 is a perfect square. √256 = 16
• the square root of 169 is 13. Therefore, the square root of 169 is an integer, and as a consequence 169 is a perfect square.
• the square root of 226 is about 15.033. Thus, the square root of 226 is not an integer, and therefore 226 is not a square number.
• The prime factors of N = 100 are 2, 2, 5, 5. Therefore, the number of factors that are perfect square are (1 + 2/2) * (1 + 2/2) = 4.
• Factor pairs: 121 = 1 × 121 or 11 × 11. 121 is a perfect square. √121 = 11.
• the square root of 299 is about 17.292. Thus, the square root of 299 is not an integer, and therefore 299 is not a square number.Positive Integer factors of 299 = 13, 23, 299 divided by 13, 23, gives no remainder.
• the square root of 324 is 18. Therefore, the square root of 324 is an integer, and as a consequence 324 is a perfect square.
• Factor pairs: 1024 = 1 × 1024, 2 × 512, 4 × 256, 8 × 128, 16 × 64, or 32 × 32, 1024 is a perfect square. √1024 = 32. It is also a perfect 5th power, and a perfect 10th power.
• 2027 is not a perfact square
• Prime factorisation of 10404 = 2 × 2 × 3 × 3 × 17 × 17. => 102. Hence, Square root of 10404 = 102.