Questions: √(7 x²) + √(3 x⁷) √(7 x²) ⋅ √(8 x⁷) =

Solution Steps

To solve the given problem, we need to multiply and simplify the square roots. We will use the property of square roots that \(\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}\).

We start with the given expressions: \[ \sqrt{7 x^{2}} \quad \text{and} \quad \sqrt{8 x^{7}} \]

First, simplify each square root expression: \[ \sqrt{7 x^{2}} = \sqrt{7} \cdot \sqrt{x^{2}} = \sqrt{7} \cdot x \] \[ \sqrt{8 x^{7}} = \sqrt{8} \cdot \sqrt{x^{7}} = 2\sqrt{2} \cdot x^{3.5} = 2\sqrt{2} \cdot x^{3} \cdot \sqrt{x} \]

Next, multiply the simplified expressions: \[ \sqrt{7} \cdot x \cdot 2\sqrt{2} \cdot x^{3} \cdot \sqrt{x} = 2\sqrt{14} \cdot x \cdot x^{3} \cdot \sqrt{x} = 2\sqrt{14} \cdot x^{4} \cdot \sqrt{x} \]

Combine the terms to get the final simplified expression: \[ 2\sqrt{14} \cdot x^{4} \cdot \sqrt{x} = 2\sqrt{14} \cdot x^{4.5} = 2\sqrt{14} \cdot x^{\frac{9}{2}} \]

Final Answer