\(\sqrt{34+24\sqrt{2}}=\sqrt{18+2.3\sqrt{2}.4+16}\)

\(=\sqrt{\left(3\sqrt{2}+4\right)^2}=3\sqrt{2}+4\)

\(\sqrt{34+24\sqrt{2}}\)

\(=\sqrt{18+2.12\sqrt{2}+16}\)

\(=\sqrt{\left(3\sqrt{2}+4\right)^2}\)

\(=3\sqrt{2}+4\)

\(=3ab^2\)

\(\sqrt{3^2a^2b^4}\)=3a\(b^2\)

\(\sqrt{\dfrac{45\left(x+y\right)^2.y^2}{16}}\left(dkxd:x\ge0,y\ge0\right)\\ =\dfrac{\sqrt{45\left(x+y\right)^2.y^2}}{\sqrt{16}}\\ =\dfrac{\sqrt{45}.\sqrt{\left(x+y\right)^2}.\sqrt{y^2}}{\sqrt{4^2}}\\ =\dfrac{\sqrt{3^2.5}.\left|x+y\right|.\left|y\right|}{4}\\ =\dfrac{3\sqrt{5}\left(x+y\right).y}{4}\\ =\dfrac{3\sqrt{5}\left(xy+y^2\right)}{4}\)

x^ 3 mà

\(\sqrt{\left(-9\right)\cdot\left(-36\right)\cdot ab^2}\)

\(=\sqrt{9\cdot36\cdot ab^2}\)

\(=3\cdot4\cdot\left|b\right|\cdot\sqrt{a}\)

\(=12\left|b\right|\cdot\sqrt{a}\)

48 y 4 = 16 . 3 y 4 = 4 . y 2 3