How do you simplify $2 x \sqrt{20 x^{20}}$ $2xsqrt(20x^20)$ ?

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Answer 1 · 2017-04-22T18:46:45

$4 x^{11} \sqrt{5}$ $4x^11sqrt5$

$2 x \sqrt{20 x^{20}}$ $2xsqrt(20x^20)$

$\sqrt{a} = a^{\frac{1}{2}}$ $sqrt(a) = a^(1/2)$

${(a^{m})}^{n} = a^{m \cdot n}$ $(a^m)^n=a^(m*n)$

using these two laws:

$\sqrt{x^{20}} = {(x^{20})}^{\frac{1}{2}}$ $sqrt(x^20) = (x^20)^(1/2)$

$= x^{\frac{20}{2}}$ $=x^(20/2)$

$= x^{10}$ $= x^10$

$\sqrt{20 x^{20}} = \sqrt{20} \cdot x^{10}$ $sqrt(20x^20) = sqrt(20) * x^10$

$\sqrt{20} = \sqrt{4} \cdot \sqrt{5} = 2 \sqrt{5}$ $sqrt(20) = sqrt(4)*sqrt(5) = 2sqrt5$

$\sqrt{20 x^{20}} = 2 \sqrt{5} \cdot x^{10}$ $sqrt(20x^20) = 2sqrt5*x^10$

$2 x \sqrt{20 x^{20}} = 2 \cdot \sqrt{5} \cdot x^{10} \cdot 2 x$ $2xsqrt(20x^20) = 2*sqrt5*x^10*2x$
$= 4 x^{11} \sqrt{5}$ $=4x^11sqrt5$

How do you simplify 2xsqrt(20x^20)2x√20x202xsqrt(20x^20)?