Question

add. write your answer in simplest form
-√98 + 4√50

Explanation:

Step1: Simplify each square root

Simplify \(-\sqrt{98}\): We factor 98 as \(49\times2\), so \(-\sqrt{98}=-\sqrt{49\times2}\). Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 49\), \(b=2\) and \(\sqrt{49} = 7\)), we get \(-\sqrt{49\times2}=- 7\sqrt{2}\).

Simplify \(4\sqrt{50}\): Factor 50 as \(25\times2\), so \(4\sqrt{50}=4\sqrt{25\times2}\). Using the same square - root property, \(\sqrt{25\times2}=\sqrt{25}\times\sqrt{2}=5\sqrt{2}\), then \(4\sqrt{25\times2}=4\times5\sqrt{2}=20\sqrt{2}\).

Step2: Combine like terms

Now we have \(-\sqrt{98}+4\sqrt{50}=-7\sqrt{2}+20\sqrt{2}\). Since the terms have the same radical part (\(\sqrt{2}\)), we can combine the coefficients: \((- 7 + 20)\sqrt{2}\).

Calculate \(-7 + 20=13\), so \((-7 + 20)\sqrt{2}=13\sqrt{2}\).

Answer:

\(13\sqrt{2}\)