$\frac{(144)^{\frac{1}{2}}+(256)^{\frac{1}{2}}}{3^2-2}$
$=\frac{(12^2)^{\frac{1}{2}}+(16^2)^{\frac{1}{2}}}{9-2}$
$=\frac{12^{2\times\frac{1}{2}}+16^{2\times\frac{1}{2}}}{7}$ $[\text{As, }(\text{x}^{\text{m}})^{\text{n}}=\text{x}^{\text{mn}}]$
$=\frac{12+16}{7}$
$=\frac{28}{7}$
$=4$
Hence, the correct alternative is option $(b).$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.