Symbolise the following statements.
The square of every real number is positive.

Answer

To symbolize the statement "The square of every real number is positive," we can follow these steps:

### Step 1: Identify the variable
Let \( x \) represent a real number.

### Step 2: Understand the statement
The statement refers to "every real number," which implies that we need to use a universal quantifier.

### Step 3: Use the universal quantifier
We express "for every real number \( x \)" using the universal quantifier \( \forall \). This can be written as:
\[ \forall x \in \mathbb{R} \]

### Step 4: Express the condition
The condition states that the square of \( x \) is positive. The square of \( x \) is \( x^2 \), and we need to express that \( x^2 \) is greater than zero:
\[ x^2 > 0 \]

### Step 5: Combine the expressions
Putting it all together, we can symbolize the entire statement as:
\[ \forall x \in \mathbb{R}, \, x^2 > 0 \]

### Final Answer
Thus, the symbolic representation of the statement "The square of every real number is positive" is:
\[ \forall x \in \mathbb{R}, \, x^2 > 0 \]

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