Question

simplify.
-5√75 + √48

Explanation:

Step1: Simplify each square root

First, factor the numbers inside the square roots into perfect squares and other factors. For \(\sqrt{75}\), we have \(75 = 25\times3\), so \(\sqrt{75}=\sqrt{25\times3}=\sqrt{25}\times\sqrt{3}=5\sqrt{3}\) (since \(\sqrt{25} = 5\)). For \(\sqrt{48}\), we have \(48 = 16\times3\), so \(\sqrt{48}=\sqrt{16\times3}=\sqrt{16}\times\sqrt{3}=4\sqrt{3}\) (since \(\sqrt{16}=4\)).

Step2: Substitute back into the original expression

Now substitute these simplified square roots back into the original expression \(-5\sqrt{75}+\sqrt{48}\). We get \(-5\times(5\sqrt{3}) + 4\sqrt{3}\).

Step3: Perform the multiplication and combine like terms

First, multiply \(-5\) and \(5\) to get \(-25\), so the expression becomes \(-25\sqrt{3}+4\sqrt{3}\). Now, combine the like terms (terms with \(\sqrt{3}\)): \((-25 + 4)\sqrt{3}=-21\sqrt{3}\).

Answer:

\(-21\sqrt{3}\)