Explanation:
To solve the expression \(\sqrt{35} \cdot 27 \cdot 6\) with the square root included, you can follow these steps:
Step 1: Simplify the square root.
\(\sqrt{35} = \sqrt{5 \cdot 7} = \sqrt{5} \cdot \sqrt{7}\)
Step 2: Substitute the simplified square root back into the expression.
\(\sqrt{35} \cdot 27 \cdot 6 = (\sqrt{5} \cdot \sqrt{7}) \cdot 27 \cdot 6\)
Step 3: Calculate the product.
\((\sqrt{5} \cdot \sqrt{7}) \cdot 27 \cdot 6 = \sqrt{5} \cdot \sqrt{7} \cdot 27 \cdot 6\)
Step 4: Calculate the remaining product.\(\sqrt{5} \cdot \sqrt{7} \cdot 27 \cdot 6 = (\sqrt{5} \cdot 27) \cdot (\sqrt{7} \cdot 6)\)
Step 5: Calculate each part of the product separately.
\(\sqrt{5} \cdot 27 = 27\sqrt{5}\)
\(\sqrt{7} \cdot 6 = 6\sqrt{7}\)
Step 6: Multiply the results.
\(27\sqrt{5} \cdot 6\sqrt{7} = 162\sqrt{5\cdot 7} = 162\sqrt{35}\)
So, \(\sqrt{35} \cdot 27 \cdot 6 = 162\sqrt{35}\).