Question

compound
calculate:

1. \\( \sqrt{108} - \sqrt{75} + \sqrt{48} = \\)
2. \\( \sqrt{64} + \sqrt3{225} - \sqrt3{125} = \\)

Explanation:

Step1: Simplify each radical

$ \sqrt{108} = \sqrt{36 \times 3} = 6\sqrt{3} $
$ \sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3} $
$ \sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} $

Step2: Compute expression 1

$ 6\sqrt{3} - 5\sqrt{3} + 4\sqrt{3} = (6-5+4)\sqrt{3} = 5\sqrt{3} $

Step3: Simplify each radical

$ \sqrt[3]{64} = 4 $, $ \sqrt{225} = 15 $, $ \sqrt[3]{125} = 5 $

Step4: Compute expression 2

$ 4 + 15 - 5 = 14 $

Answer:

1. $ 5\sqrt{3} $
2. $ 14 $