Question

simplify.
2√45

Explanation:

Step1: Factor the radicand

Factor 45 into prime factors: \( 45 = 9\times5 \), where 9 is a perfect square. So, \( \sqrt{45}=\sqrt{9\times5} \).

Step2: Use the square - root property

According to the property \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (\( a\geq0,b\geq0 \)), we have \( \sqrt{9\times5}=\sqrt{9}\times\sqrt{5} \). Since \( \sqrt{9} = 3 \), then \( \sqrt{45}=3\sqrt{5} \).

Step3: Multiply by the coefficient

We have the original expression \( 2\sqrt{45} \), substitute \( \sqrt{45}=3\sqrt{5} \) into it, we get \( 2\times3\sqrt{5}=6\sqrt{5} \).

Answer:

\( 6\sqrt{5} \)