Question

express in simplest radical form.\\(\sqrt{175} - 5\sqrt{63}\\)

Explanation:

Step1: Simplify \(\sqrt{175}\)

Factor 175: \(175 = 25\times7\). So, \(\sqrt{175}=\sqrt{25\times7}=\sqrt{25}\times\sqrt{7}=5\sqrt{7}\) (since \(\sqrt{25} = 5\)).

Step2: Simplify \(5\sqrt{63}\)

Factor 63: \(63 = 9\times7\). Then, \(\sqrt{63}=\sqrt{9\times7}=\sqrt{9}\times\sqrt{7}=3\sqrt{7}\) (since \(\sqrt{9}=3\)). So, \(5\sqrt{63}=5\times3\sqrt{7}=15\sqrt{7}\).

Step3: Substitute the simplified radicals

Now, substitute \(\sqrt{175}=5\sqrt{7}\) and \(5\sqrt{63}=15\sqrt{7}\) into the original expression:
\(\sqrt{175}-5\sqrt{63}=5\sqrt{7}-15\sqrt{7}\)

Step4: Combine like terms

Combine the terms with \(\sqrt{7}\): \(5\sqrt{7}-15\sqrt{7}=(5 - 15)\sqrt{7}=-10\sqrt{7}\)

Answer:

\(-10\sqrt{7}\)