Question

simplify.
$10\sqrt{75}$

Explanation:

Step1: Factor 75 into perfect square and other

We know that \(75 = 25\times3\), where 25 is a perfect square (\(25 = 5^2\)). So we can rewrite \(\sqrt{75}\) as \(\sqrt{25\times3}\).

Step2: Use square - root property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

According to the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\), we have \(\sqrt{25\times3}=\sqrt{25}\times\sqrt{3}\). Since \(\sqrt{25} = 5\), then \(\sqrt{25\times3}=5\sqrt{3}\).

Step3: Multiply with the coefficient 10

Now we have \(10\sqrt{75}=10\times\sqrt{75}\), and we just found that \(\sqrt{75} = 5\sqrt{3}\), so \(10\times5\sqrt{3}=50\sqrt{3}\).

Answer:

\(50\sqrt{3}\)