Question

think now: 12.15.2025
2 of 5
add and/or subtract the given.
\\(\sqrt{3} - 4\sqrt{75} - 3\sqrt{300}\\)
\\(\circ -49\sqrt{3}\\)
\\(\circ 51\sqrt{3}\\)
\\(\circ -51\sqrt{3}\\)
\\(\circ 49\sqrt{3}\\)

Explanation:

Step1: Simplify each radical

Simplify \(\sqrt{75}\): \(75 = 25\times3\), so \(\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}\). Then \( - 4\sqrt{75}=-4\times5\sqrt{3}=-20\sqrt{3}\).
Simplify \(\sqrt{300}\): \(300 = 100\times3\), so \(\sqrt{300}=\sqrt{100\times3}=10\sqrt{3}\). Then \( - 3\sqrt{300}=-3\times10\sqrt{3}=-30\sqrt{3}\).

Step2: Combine like terms

The original expression \(\sqrt{3}-4\sqrt{75}-3\sqrt{300}\) becomes \(\sqrt{3}-20\sqrt{3}-30\sqrt{3}\).
Combine the coefficients: \(1 - 20 - 30=-49\). So the result is \(-49\sqrt{3}\).

Answer:

\(-49\sqrt{3}\)