Question

simplifying radicals (guided)
score: 2/3 penalty: none
question
go step by step to reduce the radical.
(sqrt{240}) (sqrt{square}) (sqrt{square})
answer attempt 1 out of 2
you must answer all questions above in order to submit.
show examples

Explanation:

Step1: Factor 240 into perfect square and other

We know that \(240 = 16\times15\), where \(16\) is a perfect square (\(4^2\)). So we can rewrite \(\sqrt{240}\) as \(\sqrt{16\times15}\).

Step2: Use square - root property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a\geq0,b\geq0\))

According to the property \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\), when \(a = 16\) and \(b=15\), we have \(\sqrt{16\times15}=\sqrt{16}\times\sqrt{15}\).
Since \(\sqrt{16} = 4\), then \(\sqrt{240}=4\sqrt{15}\)

Answer:

\(4\sqrt{15}\) (In the blanks, the first blank is \(4\) and the second blank is \(15\))