Multiple Choice
Simplify the following.
11. Roots, Radicals, and Complex Numbers
Simplifying Radical Expressions
Multiple Choice
Simplify the following.
A
B
C
D
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 the 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 \(\sqrt{a^{2n}} = a^n\): \(\sqrt{a^6} = a^3\), \(\sqrt{b^2} = b\), and \(\sqrt{x^2} = x\).
Substitute these simplified terms back into the fraction: \(\frac{10 \cdot a^3 \cdot b}{5 \cdot x}\), then simplify the numerical fraction \(\frac{10}{5}\) to get the final simplified expression.
Related Videos
Related Practice