Question

select the correct answer.
which expression is equivalent to $10\sqrt{5}$?

a. $\sqrt{500}$
b. $\sqrt{105}$
c. $\sqrt{50}$
d. $\sqrt{15}$

Explanation:

Step1: Recall the property of square roots

We know that \(a\sqrt{b}=\sqrt{a^{2}\times b}\) (where \(a\geq0\) and \(b\geq0\)).

Step2: Apply the property to \(10\sqrt{5}\)

Here, \(a = 10\) and \(b=5\). So, \(10\sqrt{5}=\sqrt{10^{2}\times5}=\sqrt{100\times5}=\sqrt{500}\).

We can also check the other options:

• For option B: \(\sqrt{105}\) cannot be simplified to \(10\sqrt{5}\) since \(105 = 3\times5\times7\) and there is no square factor that can be taken out to get a coefficient of 10 outside the square root.
• For option C: \(\sqrt{50}=\sqrt{25\times2} = 5\sqrt{2}

eq10\sqrt{5}\).

• For option D: \(\sqrt{15}\) is already in simplest form and is not equal to \(10\sqrt{5}\).

Answer:

A. \(\sqrt{500}\)