Question

think now: 12.15.2025
3 of 5
add and/or subtract the given.
\\(\sqrt{50} - 5\sqrt{72} - 4\sqrt{200}\\)
\\(\circ -65\sqrt{2}\\)
\\(\circ 65\sqrt{2}\\)
\\(\circ -72\sqrt{2}\\)
\\(\circ 34\sqrt{2}\\)

Explanation:

Step1: Simplify each radical

Simplify $\sqrt{50}$: $\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$
Simplify $5\sqrt{72}$: $\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}$, so $5\sqrt{72}=5\times6\sqrt{2}=30\sqrt{2}$
Simplify $4\sqrt{200}$: $\sqrt{200}=\sqrt{100\times2}=10\sqrt{2}$, so $4\sqrt{200}=4\times10\sqrt{2}=40\sqrt{2}$

Step2: Substitute back and combine like terms

Original expression: $5\sqrt{2}-30\sqrt{2}-40\sqrt{2}$
Combine coefficients: $5 - 30 - 40 = -65$
Result: $-65\sqrt{2}$

Answer:

$-65\sqrt{2}$ (corresponding to the option: $-65\sqrt{2}$)