Question

question
express in simplest radical form.
\\(sqrt{6}sqrt{42}\\)

Explanation:

Step1: Use the property of square roots \(\sqrt{a}\sqrt{b}=\sqrt{ab}\)

\(\sqrt{6}\sqrt{42}=\sqrt{6\times42}\)

Step2: Calculate the product inside the square root

\(6\times42 = 252\), so we have \(\sqrt{252}\)

Step3: Factor 252 to find perfect square factors

\(252 = 36\times7\), so \(\sqrt{252}=\sqrt{36\times7}\)

Step4: Use the property \(\sqrt{ab}=\sqrt{a}\sqrt{b}\) again

\(\sqrt{36\times7}=\sqrt{36}\times\sqrt{7}\)

Step5: Simplify \(\sqrt{36}\)

\(\sqrt{36} = 6\), so we get \(6\sqrt{7}\)

Answer:

\(6\sqrt{7}\)