Question

simplify.
10√45

Explanation:

Step1: Factor 45 into prime factors

We know that \( 45 = 9\times5 \), and \( 9 = 3^2 \), so \( 45=3^{2}\times5 \).

Step2: Simplify the square root

According to the property of square roots \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \( a\geq0,b\geq0 \)) and \( \sqrt{a^{2}} = a \) (where \( a\geq0 \)), we have:
\( \sqrt{45}=\sqrt{3^{2}\times5}=\sqrt{3^{2}}\times\sqrt{5}=3\sqrt{5} \)

Step3: Multiply by 10

Now we multiply by the coefficient 10 outside the square root:
\( 10\sqrt{45}=10\times3\sqrt{5}=30\sqrt{5} \)

Answer:

\( 30\sqrt{5} \)