Question

find the smallest number by which the following number should be multiplied to obtain a perfect square numbers also find the square root of the square numbers obtained 768

Answer 1

$\\ \\ Let's\ factorize\ 768\ by\ LCM\ method. \\ \\ \\ 2\ |\underline{768} \\ 2\ |\underline{384} \\ 2\ |\underline{192} \\ 2\ |\underline{96} \\ 2\ |\underline{48} \\ 2\ |\underline{24} \\ 2\ |\underline{12} \\ 2\ |\underline{6} \\ 3\ |\underline{3} \\ 1\ |\underline{1} \\ \\ \\ 768 = 2^8 \times 3 \\ \\ \\ 2^8 \times 3 = 2^{4 \times 2} \times 3 = (2^4)^2 \times 3 = 16^2 \times 3$

$Here\ we\ can\ find\ that\ 768\ is\ 3\ multiplied\ by\ square\ of\ 16. \\ \\ If\ 3\ is\ multiplied\ with\ 16^2 \times 3,\ it\ becomes\ a\ perfect\ square. \\ \\ (16^2 \times 3 \times 3 = 16^2 \times 3^2 = (16 \times 3)^2 = 48^2) \\ \\ \therefore\ \bold{3}\ is\ the\ smallest\ number\ by\ which\ 768\ should\ be\ multiplied \\ to\ obtain\ a\ perfect\ square,\ and\ the\ square\ root\ of\ the\ square \\ obtained\ is\ \bold{48}. \\ \\ \\ Thank\ you. \\ \\ \\ \#adithyasajeevan$