Questions: Perform the indicated operation(s) and simplify. [ sqrt3 cdot sqrt30= ]

Solution Steps

To simplify the expression \(\sqrt{3} \cdot \sqrt{30}\), we can use the property of square roots that states \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\). Therefore, we first multiply the numbers under the square roots and then take the square root of the resulting product.

To simplify the expression \(\sqrt{3} \cdot \sqrt{30}\), we use the property of square roots: \[ \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} \] Substituting the given values, we have: \[ \sqrt{3} \cdot \sqrt{30} = \sqrt{3 \cdot 30} \]

Calculate the product of the numbers under the square root: \[ 3 \cdot 30 = 90 \] Thus, the expression becomes: \[ \sqrt{90} \]

Calculate the square root of 90: \[ \sqrt{90} \approx 9.487 \]

Final Answer