QuestionAugust 25, 2025

28 sqrt(250) 29) sqrt(108 x^4) 30) sqrt(245 x^7)

28 sqrt(250) 29) sqrt(108 x^4) 30) sqrt(245 x^7)
28 sqrt(250) 29) sqrt(108 x^4) 30) sqrt(245 x^7)

Solution
4.2(180 votes)

Answer

\(140 \sqrt{10}, 6x^2 \sqrt{3}, 7x^3 \sqrt{5x}\) Explanation 1. Simplify \(28 \sqrt{250}\) Factor 250 as \(250 = 25 \times 10\). Thus, \( \sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \times \sqrt{10} = 5 \sqrt{10} \). Therefore, \( 28 \sqrt{250} = 28 \times 5 \sqrt{10} = 140 \sqrt{10} \). 2. Simplify \(\sqrt{108 x^{4}}\) Factor 108 as \(108 = 36 \times 3\). Thus, \( \sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6 \sqrt{3} \). For \(x^4\), \(\sqrt{x^4} = x^2\). Therefore, \(\sqrt{108 x^{4}} = 6x^2 \sqrt{3}\). 3. Simplify \(\sqrt{245 x^{7}}\) Factor 245 as \(245 = 49 \times 5\). Thus, \( \sqrt{245} = \sqrt{49 \times 5} = \sqrt{49} \times \sqrt{5} = 7 \sqrt{5} \). For \(x^7\), \(\sqrt{x^7} = x^{3.5} = x^3 \sqrt{x}\). Therefore, \(\sqrt{245 x^{7}} = 7x^3 \sqrt{5x}\).

Explanation

1. Simplify \(28 \sqrt{250}\)<br /> Factor 250 as \(250 = 25 \times 10\). Thus, \( \sqrt{250} = \sqrt{25 \times 10} = \sqrt{25} \times \sqrt{10} = 5 \sqrt{10} \). Therefore, \( 28 \sqrt{250} = 28 \times 5 \sqrt{10} = 140 \sqrt{10} \).<br /><br />2. Simplify \(\sqrt{108 x^{4}}\)<br /> Factor 108 as \(108 = 36 \times 3\). Thus, \( \sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \times \sqrt{3} = 6 \sqrt{3} \). For \(x^4\), \(\sqrt{x^4} = x^2\). Therefore, \(\sqrt{108 x^{4}} = 6x^2 \sqrt{3}\).<br /><br />3. Simplify \(\sqrt{245 x^{7}}\)<br /> Factor 245 as \(245 = 49 \times 5\). Thus, \( \sqrt{245} = \sqrt{49 \times 5} = \sqrt{49} \times \sqrt{5} = 7 \sqrt{5} \). For \(x^7\), \(\sqrt{x^7} = x^{3.5} = x^3 \sqrt{x}\). Therefore, \(\sqrt{245 x^{7}} = 7x^3 \sqrt{5x}\).
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