Question

rút gọn biểu thức sau

a. \(\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\)

b. \(\sqrt{\left(\sqrt{2}+5\right)^2}-\sqrt{\left(\sqrt{2}-5\right)^2}\)

c. \(\sqrt{7+2\sqrt{10}-\sqrt{7-2\sqrt{10}}}\)

d. \(\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}\)

Answer 1

\(a.\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\)

\(=\sqrt{3}-1+\sqrt{3}+1=2\sqrt{3}\)

\(b.\sqrt{\left(\sqrt{2}+5\right)^2}-\sqrt{\left(\sqrt{2}-5\right)^2}\)

\(=\sqrt{2}+5-\left(\sqrt{2}-5\right)=\sqrt{2}+5-\sqrt{2}+5=10\)

- Tự làm mấy câu còn lại cho quen đi b

Answer 2

c: Sửa đề:\(\sqrt{7+2\sqrt{10}}-\sqrt{7-2\sqrt{10}}\)

\(=\sqrt{5}+\sqrt{2}-\sqrt{5}+\sqrt{2}=2\sqrt{2}\)

d: \(=\sqrt{5}-\sqrt{3}-\sqrt{5}-\sqrt{3}=-2\sqrt{3}\)