Find the value of M in the equation √((M-4)(M+4))=3

The equation "\[\sqrt{(M-4)(M+4)} = 3\]" was solved by squaring both sides, expanding, simplifying, and taking the square root to find the solutions M = 5 and M = -5.

Answer

Let’s solve the equation step-by-step:

Square both sides: To get rid of the square root, we’ll square both sides of the equation:

This simplifies to:
Expand the left side: Expand the product on the left side:
Simplify: Combine like terms:
Move constant to the right side: Add 16 to both sides:
Solve for M: Take the square root of both sides. Remember that there are two possible solutions, one positive and one negative:

Therefore, the solutions to the equation are

and

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Find the value of M in the equation √((M-4)(M+4))=3

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