Question

Simplify : $\frac{\sqrt{11\sqrt{121\sqrt{11\sqrt{121} } } } }{\sqrt{11\sqrt{121\sqrt{11}} }}$

Answer 1

Step-by-step explanation:

we know√121=11

=>

$numerator = \sqrt{11 \times 11 \sqrt{11 \times11} } = \sqrt{11 \times 11 \times 11 = 11 \sqrt{11} }$

$denominar = \sqrt{11 \times 11 \sqrt{11} } = 11 \sqrt{11}$

therefore the ans is =numerator/denominator=11√11/11√11 =1

Answer 2

Answer:

Step-by-step explanation:

$\frac{\sqrt{11\sqrt{121\sqrt{11\sqrt{121} } } } }{\sqrt{11\sqrt{121\sqrt{11}} }}\\\\= \frac{\sqrt{11\sqrt{121\sqrt{11\cdot 11 } } } }{\sqrt{11\sqrt{{11}^{2}\cdot {11}^{\frac{1}{2}}} }}\\\\= \frac{\sqrt{11\sqrt{121\cdot11 } } }{\sqrt{11\sqrt{{11}^{2+\frac{1}{2}}} }}\\= \frac{\sqrt{11\sqrt{11^3 } } }{\sqrt{11\sqrt{{11}^{2+\frac{1}{2}}} }}\\\\= \frac{\sqrt{11\cdot 11^\frac{3}{2} } }{\sqrt{11\sqrt{{11}^{\frac{5}{2}}} }}\\\\= \frac{\sqrt{11\cdot 11^\frac{3}{2}}}{\sqrt{11\cdot11^\frac{5}{4}}}$

$= \frac{{(11\cdot 11^\frac{3}{2})}^\frac{1}{2}}{{(11\cdot 11^\frac{5}{4})}^\frac{1}{2}}\\= \frac{(11^\frac{5}{2}) ^\frac{1}{2}}{(11^\frac{9}{4})^\frac{1}{2}}\\= 11^{\frac{5}{4} - \frac{9}{8}}\\= 11^\frac{1}{8}$