Evaluate 1/2*(( square root of 74)( square root of 74))

$\frac{1}{2} \cdot ((\sqrt{74}) (\sqrt{74}))$

Combine using the product rule for radicals.

$\frac{1}{2} \cdot \sqrt{74 \cdot 74}$

Write the expression using exponents.

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Multiply $74$ by $74$ .

$\frac{1}{2} \cdot \sqrt{5476}$

Rewrite $5476$ as $74^{2}$ .

$\frac{1}{2} \cdot \sqrt{74^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{1}{2} \cdot 74$

Cancel the common factor of $2$ .

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Factor $2$ out of $74$ .

$\frac{1}{2} \cdot (2 (37))$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 37)$

Rewrite the expression.

$37$

Evaluate 1/2*(( square root of 74)( square root of 74))

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