Question

question 3
simplify: (sqrt{640})
(8sqrt{10})
(160sqrt{2})
(20sqrt{2})
(64sqrt{10})

Explanation:

Step1: Factor 640 into perfect square and other

We know that \( 640 = 64\times10 \), where \( 64 \) is a perfect square (\( 8^2 = 64 \)). So we can rewrite \( \sqrt{640} \) as \( \sqrt{64\times10} \).

Step2: Use square - root property

According to the property of square roots \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \( a = 64\geq0 \) and \( b = 10\geq0 \)), we have \( \sqrt{64\times10}=\sqrt{64}\times\sqrt{10} \).
Since \( \sqrt{64} = 8 \) (because \( 8\times8 = 64 \)), then \( \sqrt{64}\times\sqrt{10}=8\sqrt{10} \).

Answer:

\( 8\sqrt{10} \) (corresponding to the option: 8√10)