Question

Rút gọn căn thức:

a)\(\sqrt{\dfrac{59}{25}+\dfrac{6}{5}\sqrt{2}}\)

b)\(\sqrt{\dfrac{129}{16}+\sqrt{2}}\)
c)\(\sqrt{\dfrac{289+4\sqrt{72}}{16}}\)

Answer 1

a) \(\sqrt{\dfrac{59}{25}+\dfrac{6}{5}\sqrt{2}}=\sqrt{2+2.\dfrac{3}{5}\sqrt{2}+\dfrac{9}{25}}=\sqrt{\left(\sqrt{2}+\dfrac{3}{5}\right)^2}\)

= / \(\sqrt{2}+\dfrac{3}{5}\) / = \(\sqrt{2}+\dfrac{3}{5}\)

b) \(\sqrt{\dfrac{129}{16}+\sqrt{2}}=\sqrt{8+2.2\sqrt{2}.\dfrac{1}{4}+\dfrac{1}{16}}\)

= \(\sqrt{\left(2\sqrt{2}+\dfrac{1}{4}\right)^2}\) = / \(2\sqrt{2}+\dfrac{1}{4}\) / = \(2\sqrt{2}+\dfrac{1}{4}\)

c) Tương tự , mình bận rồi , nếu chưa biết tẹo mk làm cho.

Answer 2

c) \(\sqrt{\dfrac{289+4\sqrt{72}}{16}}=\sqrt{\dfrac{289}{16}+\dfrac{1}{4}\sqrt{72}}=\sqrt{\dfrac{289}{16}+\dfrac{1}{4}.6\sqrt{2}}=\sqrt{18+2.\dfrac{1}{4}.3\sqrt{2}+\dfrac{1}{16}}=\sqrt{\left(3\sqrt{2}+\dfrac{1}{4}\right)^2}\) = / \(3\sqrt{2}+\dfrac{1}{4}\) / = \(3\sqrt{2}+\dfrac{1}{4}\)