What is this expression in simplified form? $$ 5 \sqrt{2} \cdot 9 \sqrt{6} $$ A. 90 B. $$ 90 \sqrt{3} $$ C. $$ 45 \sqrt{3} $$ D. $$ 45 \sqrt{2} $$

Question

UpStudy AI · Accepted Answer

We start with the expression:
$$
5 \sqrt{2} \cdot 9 \sqrt{6}
$$

1. Multiply the coefficients:
   $$
   5 \cdot 9 = 45
   $$

2. Multiply the radicals using the property $$\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$$:
   $$
   \sqrt{2} \cdot \sqrt{6} = \sqrt{12}
   $$

3. Simplify $$\sqrt{12}$$ by factoring out a perfect square:
   $$
   \sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3}
   $$

4. Combine the results:
   $$
   45 \cdot 2\sqrt{3} = 90\sqrt{3}
   $$

Thus, the simplified form is $$\boxed{90\sqrt{3}}$$.
The simplified form is $$90\sqrt{3}$$.

What is this expression in simplified form? \[ 5 \sqrt{2} \cdot 9 \sqrt{6} \] A. 90 B. \( 90 \sqrt{3} \) C. \( 45 \sqrt{3} \) D. \( 45 \sqrt{2} \)