Question

simplify the radical.
$5\sqrt{24} = \square$

Explanation:

Step1: Factor the radicand

Factor 24 into a product of a perfect square and another number: \(24 = 4\times6\), so \(\sqrt{24}=\sqrt{4\times6}\).

Step2: Use the property of square roots

Using the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (where \(a = 4\), \(b = 6\) and \(a\) is a perfect square), we get \(\sqrt{4\times6}=\sqrt{4}\times\sqrt{6}\). Since \(\sqrt{4} = 2\), this simplifies to \(2\sqrt{6}\).

Step3: Multiply by the coefficient

Now, multiply by the coefficient 5: \(5\times2\sqrt{6}=10\sqrt{6}\).

Answer:

\(10\sqrt{6}\)