Question

express in simplest radical form. 9√192 − 7√48 answer attempt 1 out of 2 submit answer √

Explanation:

Step1: Simplify \(\sqrt{192}\)

Factor 192: \(192 = 64\times3\), so \(\sqrt{192}=\sqrt{64\times3}=\sqrt{64}\times\sqrt{3}=8\sqrt{3}\)

Step2: Simplify \(\sqrt{48}\)

Factor 48: \(48 = 16\times3\), so \(\sqrt{48}=\sqrt{16\times3}=\sqrt{16}\times\sqrt{3}=4\sqrt{3}\)

Step3: Substitute back into the original expression

\(9\sqrt{192}-7\sqrt{48}=9\times8\sqrt{3}-7\times4\sqrt{3}\)

Step4: Calculate the coefficients

\(9\times8\sqrt{3}=72\sqrt{3}\), \(7\times4\sqrt{3}=28\sqrt{3}\)

Step5: Subtract the two terms

\(72\sqrt{3}-28\sqrt{3}=(72 - 28)\sqrt{3}=44\sqrt{3}\)

Answer:

\(44\sqrt{3}\)