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Chapter 7: Problem 8

If \(x=\sqrt{25}\), which of the following is true? $$ \begin{aligned} & \text { C } x=5 \\ & x=-5 \\ & x=\pm 5 \\ & \text { I don't know. } \\ & \end{aligned} $$

Short Answer

Expert verified
\(x = 5\) is the correct answer.

Step by step solution

01

Define the Problem

The problem enquires about the value of \(x\) when \(x=\sqrt{25}\). The crucial point to show in detail here is calculating the square root of 25.
02

Calculate Square Root

From the known knowledge, the square root of 25 is either 5 or -5. However, as per definition in mathematics and as is commonly accepted, when a square root is considered with no sign value provided the result is always considered to be positive. As there is no negative sign in front of the square root symbol, the answer is considered to be positive. Therefore, \(x = 5\).
03

Answer the Question

Among the multiple choices provided in the question, \(x = 5\) is the correct statement. Other statements are untrue based on conventional mathematics principles. The statement \(x = -5\) is incorrect because the square root of a number is always positive in the real number system. The statement \(x = \pm 5\) is incorrect because the square root is positive when no sign is mentioned. Therefore, the answer is option C, \(x = 5\).

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