+23254 Since 648 = 4 x 81 x 2,
√( 648 ) = √( 4 x 81 x 2) = √4 x √81 x √2 = 2 x 9 x √2 = 18√2
Prime factor 648.
$${\frac{{\mathtt{648}}}{{\mathtt{2}}}} = {\mathtt{324}}$$
$${\frac{{\mathtt{324}}}{{\mathtt{2}}}} = {\mathtt{162}}$$
$${\frac{{\mathtt{162}}}{{\mathtt{2}}}} = {\mathtt{81}}$$
$${\frac{{\mathtt{81}}}{{\mathtt{3}}}} = {\mathtt{27}}$$
$${\frac{{\mathtt{27}}}{{\mathtt{3}}}} = {\mathtt{9}}$$
$${\frac{{\mathtt{9}}}{{\mathtt{3}}}} = {\mathtt{3}}$$
$${{\mathtt{2}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{{\mathtt{4}}} = {\mathtt{648}}$$
2^3 can be rewritten as 2^2 * 2^1, one 2 stays in the radical.
3^4 can be taken completely taken out of the radical as 9.
Which becomes 2*9 √2 or 18*√2
