Question

add. write your answer in simplest form.
-9√128 + 10√72

Explanation:

Step1: Simplify \(\sqrt{128}\)

Factor 128: \(128 = 64\times2\), so \(\sqrt{128}=\sqrt{64\times2}=\sqrt{64}\times\sqrt{2}=8\sqrt{2}\). Then \(-9\sqrt{128}=-9\times8\sqrt{2}=-72\sqrt{2}\).

Step2: Simplify \(\sqrt{72}\)

Factor 72: \(72 = 36\times2\), so \(\sqrt{72}=\sqrt{36\times2}=\sqrt{36}\times\sqrt{2}=6\sqrt{2}\). Then \(10\sqrt{72}=10\times6\sqrt{2}=60\sqrt{2}\).

Step3: Add the simplified terms

\(-72\sqrt{2}+60\sqrt{2}=(-72 + 60)\sqrt{2}=-12\sqrt{2}\).

Answer:

\(-12\sqrt{2}\)