Question

add. write your answer in simplest form. -7√72 + 3√98

Explanation:

Step1: Simplify each radical

First, simplify \(\sqrt{72}\). We know that \(72 = 36\times2\), so \(\sqrt{72}=\sqrt{36\times2}=\sqrt{36}\times\sqrt{2}=6\sqrt{2}\) (since \(\sqrt{36} = 6\)). Then, simplify \(\sqrt{98}\). We have \(98 = 49\times2\), so \(\sqrt{98}=\sqrt{49\times2}=\sqrt{49}\times\sqrt{2}=7\sqrt{2}\) (since \(\sqrt{49}=7\)).

Step2: Substitute back into the original expression

Substitute the simplified radicals into \(-7\sqrt{72}+3\sqrt{98}\). We get \(-7\times6\sqrt{2}+3\times7\sqrt{2}\).

Step3: Calculate each term

For the first term: \(-7\times6\sqrt{2}=-42\sqrt{2}\). For the second term: \(3\times7\sqrt{2}=21\sqrt{2}\).

Step4: Combine like terms

Now, combine \(-42\sqrt{2}\) and \(21\sqrt{2}\). So, \(-42\sqrt{2}+21\sqrt{2}=(-42 + 21)\sqrt{2}=-21\sqrt{2}\).

Answer:

\(-21\sqrt{2}\)