Evaluate square root of 54

Problem

$\sqrt{54}$

Solution

1. Identify the radicand and look for the largest perfect square factor of 54.

2. Factor the number 54 into a product of a perfect square and another integer.

$54=9\cdot 6$

3. Apply the product property of square roots, which states that $\sqrt{a\cdot b}=\sqrt{a}\cdot \sqrt{b}$

$\sqrt{54}=\sqrt{9\cdot 6}$

$\sqrt{54}=\sqrt{9}\cdot \sqrt{6}$

4. Simplify the square root of the perfect square.

$\sqrt{9}=3$

5. Combine the results to write the expression in simplest radical form.

$\sqrt{54}=3\sqrt{6}$

Final Answer

$\sqrt{54}=3\sqrt{6}$

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