Question

which expression is equivalent to \\(\sqrt{600}\\)?
a. \\(10\sqrt{6}\\)
b. \\(24\sqrt{25}\\)
c. \\(25\sqrt{24}\\)
d. \\(6\sqrt{10}\\)

Explanation:

Step1: Factor 600

We know that \( 600 = 100\times6 \), where 100 is a perfect square.

Step2: Apply square root property

Using the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (for \( a\geq0, b\geq0 \)), we have \( \sqrt{600}=\sqrt{100\times6}=\sqrt{100}\times\sqrt{6} \).

Step3: Simplify \( \sqrt{100} \)

Since \( \sqrt{100} = 10 \), then \( \sqrt{600}=10\sqrt{6} \).

Answer:

A. \( 10\sqrt{6} \)