Multiple Choice
Simplify the following.
9. Roots, Radicals, and Complex Numbers
Simplifying Radical Expressions
Multiple Choice
Simplify the following.
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Verified step by step guidance1
Start with the expression under the square root: \(\sqrt{\frac{100a^6b^2}{25x^2}}\).
Rewrite the square root of a fraction as the fraction of square roots: \(\frac{\sqrt{100a^6b^2}}{\sqrt{25x^2}}\).
Simplify the square roots of the numerical coefficients: \(\sqrt{100} = 10\) and \(\sqrt{25} = 5\), so the expression becomes \(\frac{10\sqrt{a^6b^2}}{5\sqrt{x^2}}\).
Simplify the square roots of the variable expressions by using the property \(\sqrt{m^2} = m\) for even powers: \(\sqrt{a^6} = a^3\), \(\sqrt{b^2} = b\), and \(\sqrt{x^2} = x\).
Combine all simplified parts to write the expression as \(\frac{10 a^3 b}{5 x}\), then reduce the fraction \(\frac{10}{5}\) to its simplest form.
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