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Complete The Pattren
√3, √12, √27, √48, ......

User Spacetyper
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1 Answer

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Final answer:

The pattern under the square root is a product of 3 and consecutive perfect squares. The next number in the sequence is the square root of 3 multiplied by 5 squared, which is √75.

Step-by-step explanation:

To complete the pattern √3, √12, √27, √48, ......, we should look for a relationship between the numbers under the square root. Let's examine the pattern they form:

  • The first number is √3, which we can also write as √(3×1).
  • The second number is √12, which we can write as √(3×4).
  • The third number is √27, which we can write as √(3×9).
  • The fourth number is √48, which can be written as √(3×16).

Looking at this pattern, we notice that the multiplier of 3 is increasing by 3 each time (1, 4, 9, 16,...), which are perfect squares (1^2, 2^2, 3^2, 4^2,...).

The next number in the sequence would be 5^2 since we are incrementing the perfect squares by 1 sequentially. Therefore, the next number in the pattern is √(3×25) or √75.

User Brian De Alwis
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