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Mathematics

Find the square root of 108612110\dfrac{86}{121} by prime factorisation method.

Sq & Sq Roots

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Answer

1086121=1296121=1296121=(2×2)×(2×2)×(3×3)×(3×3)(11×11)=2×2×3×311=3611=3311\sqrt{10\dfrac{86}{121}}\\[1em] = \sqrt{\dfrac{1296}{121}}\\[1em] = {\dfrac{\sqrt{1296}}{\sqrt{121}}}\\[1em] = {\dfrac{\sqrt{(2\times2)\times(2\times2)\times(3\times3)\times(3\times3)}}{\sqrt{(11\times11)}}}\\[1em] = {\dfrac{2\times2\times3\times3}{11}}\\[1em] = {\dfrac{36}{11}}\\[1em] = 3{\dfrac{3}{11}}

Hence, 1086121=3311\sqrt{10\dfrac{86}{121}}= 3{\dfrac{3}{11}}

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