# How do you solve the equation and identify any extraneous solutions for #sqrt(x-3) =1#?

The term under the root must be

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To solve the equation sqrt(x-3) = 1, we need to isolate the variable x.

First, square both sides of the equation to eliminate the square root: (sqrt(x-3))^2 = 1^2.

This simplifies to x-3 = 1.

Next, add 3 to both sides of the equation to isolate x: x-3+3 = 1+3.

This simplifies to x = 4.

To identify any extraneous solutions, we need to check if the obtained solution satisfies the original equation.

Substituting x = 4 back into the original equation sqrt(x-3) = 1, we get sqrt(4-3) = 1, which simplifies to sqrt(1) = 1.

Since the square root of 1 is indeed 1, the solution x = 4 is valid and there are no extraneous solutions.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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