41. The simplified value of (√3 + 1) (10 + $$\sqrt {12} $$ ) ($$\sqrt {12} $$ - 2) (5 - √3) is
42. Which one among $$\root 3 \of 6 ,\,\root 2 \of 5 $$ and $$\root 6 \of {12} $$ is the largest?
43. The value of $$\frac{{{{\left( {243} \right)}^{\frac{n}{5}}} \times {3^{2n + 1}}}}{{{9^n} \times {3^{n - 1}}}}$$ is?
44. The value of $$\frac{{\sqrt {72} \times \sqrt {363} \times \sqrt {175} }}{{\sqrt {32} \times \sqrt {147} \times \sqrt {252} }}$$ is?
45. (3x - 2y) : (2x + 3y) = 5 : 6, then one of the value of $${\left( {\frac{{\root 3 \of x + \root 3 \of y }}{{\root 3 \of x - \root 3 \of y }}} \right)^2}$$ is?
46. If a, b are rationals and a√2 + b√3 = $$\sqrt {98} + \sqrt {108} - \sqrt {48} - \sqrt {72} ,$$ then the values of a, b are respectively
47. What is the value of $$\frac{{\sqrt 7 + \sqrt 5 }}{{\sqrt 7 - \sqrt 5 }} \div \frac{{\sqrt {14} + \sqrt {10} }}{{\sqrt {14} - \sqrt {10} }} + \frac{{\sqrt {10} }}{{\sqrt 5 }}?$$
48. 3x - 3x - 1 = 486, Find x
49. If 5√3 + $$\sqrt {75} $$ = 17.32, then the value of 14√3 + $$\sqrt {108} $$ is.
50. Which of the following is true?
$$\eqalign{
& {\text{I}}.\root 3 \of {11} > \sqrt 7 > \root 4 \of {45} \cr
& {\text{II}}.\sqrt 7 > \root 3 \of {11} > \root 4 \of {45} \cr
& {\text{III}}.\sqrt 7 > \root 4 \of {45} > \root 3 \of {11} \cr
& {\text{IV}}.\root 4 \of {45} > \sqrt 7 > \root 3 \of {11} \cr} $$
$$\eqalign{ & {\text{I}}.\root 3 \of {11} > \sqrt 7 > \root 4 \of {45} \cr & {\text{II}}.\sqrt 7 > \root 3 \of {11} > \root 4 \of {45} \cr & {\text{III}}.\sqrt 7 > \root 4 \of {45} > \root 3 \of {11} \cr & {\text{IV}}.\root 4 \of {45} > \sqrt 7 > \root 3 \of {11} \cr} $$
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