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9) \( \sqrt{128 x^{6}}+\sqrt{98 x} 6 \)

Ask by Evans Flynn. in South Africa
Feb 03,2025

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The simplified expression is \(8x^3 \sqrt{2} + 42 \sqrt{2x}\).

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To simplify \( \sqrt{128 x^{6}}+\sqrt{98 x} 6 \), let's break down each term: The first term \( \sqrt{128 x^6} \) simplifies as follows: 1. \( 128 = 64 \times 2 \), where \( 64 \) is a perfect square. 2. Thus, \( \sqrt{128 x^6} = \sqrt{64} \times \sqrt{2} \times \sqrt{x^6} = 8x^3\sqrt{2} \). The second term \( \sqrt{98 x} \): 1. \( 98 = 49 \times 2 \), where \( 49 \) is a perfect square. 2. So, \( \sqrt{98 x} = \sqrt{49} \times \sqrt{2} \times \sqrt{x} = 7\sqrt{2}\sqrt{x} = 7\sqrt{2x} \). Now, multiply the second term by 6: \( \sqrt{98 x} \cdot 6 = 6 \times 7\sqrt{2x} = 42\sqrt{2x} \). Putting it all together, we have: \[ 8x^3\sqrt{2} + 42\sqrt{2x}. \] To see if we can combine terms, note that both terms contain \( \sqrt{2} \), but since the variables are different, we can't combine them directly. So the simplified expression is \( 8x^3\sqrt{2} + 42\sqrt{2x} \).

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