Evaluate:
5[234−310]\sqrt{5\Big[2\dfrac{3}{4} - \dfrac{3}{10}\Big]}5[243−103]
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5[234−310]=5[114−310]\sqrt{5\Big[2\dfrac{3}{4} - \dfrac{3}{10}\Big]}\\[1em] = \sqrt{5\Big[\dfrac{11}{4} - \dfrac{3}{10}\Big]}5[243−103]=5[411−103]
LCM of 4 and 10 is 2 x 2 x 5 = 20.
=5[11×54×5−3×210×2]=5[5520−620]=5[55−620]=5[4920]=[5×4920]=[494]=[7×72×2]=72=312= \sqrt{5\Big[\dfrac{11\times 5}{4 \times 5} - \dfrac{3 \times 2}{10 \times 2}\Big]}\\[1em] = \sqrt{5\Big[\dfrac{55}{20} - \dfrac{6}{20}\Big]}\\[1em] = \sqrt{5\Big[\dfrac{55 - 6}{20}\Big]}\\[1em] = \sqrt{5\Big[\dfrac{49}{20}\Big]}\\[1em] = \sqrt{\Big[\dfrac{5 \times 49}{20}\Big]}\\[1em] = \sqrt{\Big[\dfrac{49}{4}\Big]}\\[1em] = \sqrt{\Big[\dfrac{7 \times 7}{2 \times 2}\Big]}\\[1em] = \dfrac{7}{2}\\[1em] = 3\dfrac{1}{2}=5[4×511×5−10×23×2]=5[2055−206]=5[2055−6]=5[2049]=[205×49]=[449]=[2×27×7]=27=321
5[234−310]=312\sqrt{5\Big[2\dfrac{3}{4} - \dfrac{3}{10}\Big]} = 3\dfrac{1}{2}5[243−103]=321
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