Tính giá trị biểu thức:
a)\(\sqrt{6-4\sqrt{2}}+\sqrt{19-6\sqrt{2}}\)
b)\(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)
c)\(\sqrt{7-2\sqrt{10}}-\sqrt{6-2\sqrt{5}}\)
Tính giá trị biểu thức:
a)\(\sqrt{6-4\sqrt{2}}+\sqrt{19-6\sqrt{2}}\)
b)\(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)
c)\(\sqrt{7-2\sqrt{10}}-\sqrt{6-2\sqrt{5}}\)
a) \(\sqrt{6-4\sqrt{2}}+\sqrt{19-6\sqrt{2}}\)\(=\sqrt{4-4\sqrt{2}+2}+\sqrt{18-2.3\sqrt{2}.1+1}=\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(3\sqrt{2}-1\right)^2}\)
=\(\sqrt{\left(2-\sqrt{2}\right)^2}+\sqrt{\left(3\sqrt{2}-1\right)^2}\)
= | 2 – \(\sqrt{2}\) | + | 3\(\sqrt{2}\) – 1|
= 2 – \(\sqrt{2}\) + 3\(\sqrt{2}\) – 1
= 2\(\sqrt{2}\) + 1
b) \(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)
\(=\sqrt{45-2.3.\sqrt{5}+1}-\sqrt{20-2.3.2.\sqrt{5}+9}\)
\(=\sqrt{\left(3\sqrt{5}-1\right)^2}-\sqrt{\left(2\sqrt{5}-3\right)^2}\)
= | 3\(\sqrt{5}\) – 1| – | 2\(\sqrt{5}\) – 3|
= 3\(\sqrt{5}\) – 1 – 2\(\sqrt{5}\) + 3
= \(\sqrt{5}\) + 2
c) \(\sqrt{7-2\sqrt{10}}-\sqrt{6-2\sqrt{5}}\)
\(=\sqrt{5-2\sqrt{5}.\sqrt{2}+2}-\sqrt{5-2\sqrt{5}+1}\)
\(=\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{5}-1\right)^2}\)
= | \(\sqrt{5}\) – \(\sqrt{2}\) | – | \(\sqrt{5}\) – 1 |
= 1 – \(\sqrt{2}\)
Mik làm lun không chép đề ạ
a) `sqrt{(2 – √2)²}` + `sqrt{(3√2 – 1)²}`
`= 2 – √2 + 3√2 – 1`
`= 2√2 – 1`
b) `sqrt{46 – 6√5}` – `sqrt{29 – 12√5}`
= `sqrt{(3√5 – 1)²}` – `sqrt{(3 – 2√5)²}`
`= 3√5 – 1 – 2√5 + 3`
`= √5 + 2`
c) `sqrt{(√5 – √2)²}` – `sqrt{(1 – √5)²}`
`= √5 – √2 – √5 + 1`
`= 1 – √2`