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Mathematics

Find the square root of 108×2028\sqrt{108 \times 2028}.

Sq & Sq Roots

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Answer

108×2028=108×2028=3×36×3×676=3×36×3×676=3×6×3×26=(3×3)×6×26=3×6×26=468\sqrt{108 \times 2028}\\[1em] = \sqrt{108} \times \sqrt{2028}\\[1em] = \sqrt{3 \times 36} \times \sqrt{3 \times 676}\\[1em] = \sqrt{3} \times \sqrt{36} \times \sqrt{3} \times \sqrt{676}\\[1em] = \sqrt{3} \times 6 \times \sqrt{3} \times 26\\[1em] = (\sqrt{3} \times \sqrt{3}) \times 6 \times 26\\[1em] = 3 \times 6 \times 26\\[1em] = 468

Hence, 108×2028=468\sqrt{108 \times 2028} = 468.

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