rút gọn biểu thức `(sqrt{14}-sqrt{2}) sqrt{4+sqrt{7}}`
2 câu trả lời
($\sqrt{14}$ - $\sqrt{2}$).$\sqrt{4 + \sqrt{7}}$
= $\sqrt{2}$.($\sqrt{7}$ - 1).$\sqrt{\frac{2.(4 + \sqrt{7})}{2}}$
= $\sqrt{2}$.($\sqrt{7}$ - 1).$\sqrt{\frac{8 + 2\sqrt{7}}{2}}$
= $\sqrt{2}$.($\sqrt{7}$ - 1).$\sqrt{\frac{7 + 2\sqrt{7} + 1}{2}}$
= $\sqrt{2}$.($\sqrt{7}$ - 1).$\sqrt{\frac{(\sqrt{7} + 1)²}{2}}$
= $\sqrt{2}$.($\sqrt{7}$ - 1).$\frac{|\sqrt{7} + 1|}{\sqrt{2}}$
= $\sqrt{2}$.($\sqrt{7}$ - 1).$\frac{\sqrt{7} + 1}{\sqrt{2}}$
= ($\sqrt{7}$ - 1).($\sqrt{7}$ + 1)
= 7 - 1
= 6
Chúc bạn học tốt
($\sqrt{14}$-$\sqrt{2}$).$\sqrt{4+\sqrt{7}}$
`=` $\sqrt{(\sqrt{14}-\sqrt{2})².(4+\sqrt{7}}$
`=` $\sqrt{(16-4\sqrt{7})(4+\sqrt{7}}$
`= 2`$\sqrt{4²-(\sqrt{7})²}$
`= 2`$\sqrt{16-7}$
`= 6`
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