How can 10sqrt48 be simplified?

Question

10sqrt48 = 40sqrt3
how is this calculated?

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Answer 1 · 2018-03-20T06:49:06

$40 \sqrt{3}$ $color(brown)( 40sqrt3$

$10 \sqrt{48} = 10 \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 3}, factorising 48$ $10 sqrt48 = 10 sqrt(2 * 2 * 2 * 2 * 3), " factorising 48"$

$\Rightarrow 10 \sqrt{2^{4} \cdot 3} = 10 \cdot 2^{2} \sqrt{3}$ $=> 10 sqrt(2^4 * 3) = 10 * 2^2 sqrt3$

$\Rightarrow 10 \cdot 4 \sqrt{3} = 40 \sqrt{3}$ $=> 10 * 4 sqrt3 = 40sqrt3$