Question

problem 19
simplify \\(\sqrt{405}\\)
a. 20.5
b. \\(5\sqrt{40}\\)
c. \\(9\sqrt{45}\\)
d. \\(9\sqrt{5}\\)

Explanation:

Step1: Factor 405 into perfect square and other factor

We know that \(405 = 81\times5\), where \(81\) is a perfect square (\(9^2 = 81\)). So we can rewrite \(\sqrt{405}\) as \(\sqrt{81\times5}\).

Step2: Use the property of square roots \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

Applying the property, \(\sqrt{81\times5}=\sqrt{81}\times\sqrt{5}\).

Step3: Simplify \(\sqrt{81}\)

Since \(\sqrt{81} = 9\) (because \(9\times9 = 81\)), we get \(9\times\sqrt{5}=9\sqrt{5}\).

Answer:

D. \(9\sqrt{5}\)