61. The simplified value of
$$\frac{{\sqrt {32} + \sqrt {48} }}{{\sqrt 8 + \sqrt {12} }}{\text{ is = ?}}$$
62. Number of digits in the square root of 62478078 is = ?
63. $${\text{If }}\left( {{n^r} - tn + \frac{1}{4}} \right)$$ be a perfect square, then the values of t are = ?
64. If x = a + m, y = b + m, z = c + m, then the value of $$\frac{{{x^2} + {y^2} + {z^2} - yz - zx - xy}}{{{a^2} + {b^2} + {c^2} - ab - bc - ca}}$$ is = ?
65. $$\left( {\frac{{785 \times 785 \times 785 + 435 \times 435 \times 435}}{{785 \times 785 + 435 \times 435 - 785 \times 435}}} \right)$$ simplifies to = ?
66. $$\frac{{38 \times 38 \times 38 + 34 \times 34 \times 34 + 28 \times 28 \times 28 - 38 \times 34 \times 84}}{{38 \times 38 + 34 \times 34 + 28 \times 28 - 38 \times 34 - 34 \times 28 - 38 \times 28}}$$ is equal to = ?
67. The greatest 4 digit number which is a perfect square, is = ?
68. What number must be added to the expression 16a2 - 12a to make a perfect square ?
69. A teacher wants to arrange his students in an equal number of rows and columns. If there are 1369 students, the number of students in the last row are ?
70. The value of $$\frac{{{{\left( {x - y} \right)}^3} + {{\left( {y - z} \right)}^3} + {{\left( {z - x} \right)}^3}}}{{{{\left( {{x^2} - {y^2}} \right)}^3} + {{\left( {{y^2} - {z^2}} \right)}^3} + {{\left( {{z^2} - {x^2}} \right)}^3}}}$$ is = ?
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