Question

select the correct answer.
what is this expression in simplified form?
$(6\sqrt{2})\\ (-3\sqrt{5})$
\\(\bigcirc\\) a. \\(-90\\)
\\(\bigcirc\\) b. \\(-18\sqrt{10}\\)
\\(\bigcirc\\) c. \\(-18\sqrt{7}\\)
\\(\bigcirc\\) d. \\(3\sqrt{7}\\)

Explanation:

Step1: Multiply the coefficients

Multiply 6 and -3: \(6\times(-3)= -18\)

Step2: Multiply the radicals

Multiply \(\sqrt{2}\) and \(\sqrt{5}\) using the property \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\): \(\sqrt{2}\times\sqrt{5}=\sqrt{2\times5}=\sqrt{10}\)

Step3: Combine the results

Multiply the results from Step1 and Step2: \(-18\times\sqrt{10}=-18\sqrt{10}\)

Answer:

B. \(-18\sqrt{10}\)