Question

select the correct answer.
simplify.
√75
a. 3√5
b. 15√5
c. 25√3
d. 5√3

Explanation:

Step1: Factor 75 into perfect square and other factor

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 the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (for \(a\geq0,b\geq0\))

Applying the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\), we get \(\sqrt{25\times3}=\sqrt{25}\times\sqrt{3}\).
Since \(\sqrt{25} = 5\) (because \(5^2=25\)), then \(\sqrt{25}\times\sqrt{3}=5\sqrt{3}\).

Answer:

D. \(5\sqrt{3}\)