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What is the missing number in the grid: [[16, 9, 4], [25, 16, 9], [36, 25, ?]]?

Mathematics

ScanSolve AI Answer

Answer

D

Step-by-step solution

6 steps
  1. Observe the numbers in the grid.

    The numbers in the grid are:

    [1694251693625?]\begin{bmatrix} 16 & 9 & 4 \\ 25 & 16 & 9 \\ 36 & 25 & ? \end{bmatrix}

    Notice that all the visible numbers are perfect squares.

  2. Find the square root of each number in the grid.

    Let's find the square roots for each cell:

    [1694251693625?]=[43254365?]\begin{bmatrix} \sqrt{16} & \sqrt{9} & \sqrt{4} \\ \sqrt{25} & \sqrt{16} & \sqrt{9} \\ \sqrt{36} & \sqrt{25} & \sqrt{?} \end{bmatrix} = \begin{bmatrix} 4 & 3 & 2 \\ 5 & 4 & 3 \\ 6 & 5 & ? \end{bmatrix}
  3. Identify the pattern in the square roots.

    Looking at the square roots:

    • In the first row, the numbers are $4, 3, 2$ (decreasing by 1).
    • In the second row, the numbers are $5, 4, 3$ (decreasing by 1).
    • This pattern suggests that in each row, the numbers decrease by 1 from left to right.
  4. Apply the pattern to find the missing square root.

    Following the pattern for the third row, the numbers should be 6,5,(5−1)6, 5, (5-1).
    So, the missing square root is 5−1=45-1=4.

  5. Calculate the missing number.

    The missing number is the square of the missing square root:

    ?=42=16? = 4^2 = 16
  6. Compare with the given options.

    The calculated missing number is 16.
    The options are: a. 49, b. 25, c. 9, d. 16.
    The correct option is d.

    The final answer is d. 16\boxed{\text{d. 16}}.

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