Lời giải:
\(\sqrt{11+\sqrt{7}}-\sqrt{(-1+\sqrt{7})^2}=\sqrt{11+\sqrt{7}}-|-1+\sqrt{7}|\)
\(=\sqrt{11+\sqrt{7}}-(-1+\sqrt{7})=\sqrt{11+\sqrt{7}}+1-\sqrt{7}\)
a) 11+6\(\sqrt{2}\) = \(\left(3+\sqrt{2}\right)^2\)
b) 8-2\(\sqrt{7}\)=\(\left(\sqrt{7}-1\right)^2\)
c)\(\sqrt{11+6\sqrt{2}}=\sqrt{11-6\sqrt{2}}=6\)
d) \(\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}=-2\)
Rút gọn: (Giải chi tiết từng bước)
7) \(\left(\sqrt{28}-\sqrt{12}-\sqrt{7}\right)\sqrt{7}+2\sqrt{21}\)
8) \(\left(\sqrt{99}-\sqrt{18}-\sqrt{11}\right)\sqrt{11}+3\sqrt{22}\)
\(\sqrt{\left(\sqrt{7}-5\right)^2}+\sqrt{\left(2-\sqrt{7}\right)^2}\)
\(\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
\(\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}\)
\(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
Câu 1
1) Tính
a) \(\sqrt{25}+\sqrt{49}\) b) \(\sqrt{121}-\sqrt{81}\)
2) Với x > -2 thì \(\sqrt{2x+1}\) có nghĩa không
3) Rút gọn biểu thức sau :
a) \(\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{3}\) b) \(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right)\sqrt{7}+7\sqrt{8}\) c) \(\dfrac{\sqrt{27}-\sqrt{108}+\sqrt{12}}{\sqrt{3}}\)
1) \(\left(\sqrt{6}-\sqrt{8}\right)\left(\sqrt{6}+\sqrt{8}\right).\)
2)\(\left(3-\sqrt{5}\right)\left(3+\sqrt{5}\right)\)
3)\(\sqrt{7-4\sqrt{3}}+\sqrt{7+4\sqrt{3}}\)
4)\(\sqrt{2\sqrt{3}-4}+\sqrt{2\sqrt{3}+4}\)
5)\(\sqrt{4\sqrt{6}+11}-\sqrt{11-4\sqrt{6}}\)
6)\(\sqrt{10+2\sqrt{11}}-\sqrt{10-2\sqrt{11}}\)
7)\(\sqrt{5-2\sqrt{7-2\sqrt{6}}}\)
AI ĐÓ TỐT BỤNG GIÚP MK ZỚI:((
\(\sqrt{\left(11-6\sqrt{2}\right)^2}+\sqrt{\left(11+6\sqrt{2}\right)^2}\)
\(\sqrt{\left(10-4\sqrt{6}\right)^2}-\sqrt{\left(10+4\sqrt{6}\right)^2}\)
\(\sqrt{\left(4-\sqrt{5}\right)^2}+\sqrt{\left(1-\sqrt{5}\right)^2}\)
\(\sqrt{\left(7+\sqrt{2}\right)^2}-\sqrt{\left(1-\sqrt{2}\right)^2}\)
Tính:
1) ( \(2\sqrt{5}-\sqrt{7}\) ) \(\left(2\sqrt{5}+\sqrt{7}\right)\)
2) \(\left(5\sqrt{2}+2\sqrt{3}\right)\left(2\sqrt{3}-5\sqrt{2}\right)\)
3) \(\sqrt{\left(\sqrt{7}-2\right)^2}+\sqrt{\left(\sqrt{7}+2\right)^2}\)
4) \(\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)
5) \(\left(\sqrt{5}-\sqrt{6}\right)^2\)
6) \(\left(\sqrt{3}-\sqrt{5}\right)^2\)
7) \(\left(2\sqrt{2}+\sqrt{3}\right)^2\)
* Tính
a. A=\(\left(\dfrac{6+\sqrt{20}}{3+\sqrt{5}}+\dfrac{\sqrt{14}-\sqrt{2}}{\sqrt{7}-1}\right):\left(2+\sqrt{2}\right)\)
b. B=\(\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}-\dfrac{11}{2\sqrt{3}+1}\)
Giải phương trình:
e) \(\sqrt{x^2}=\left|-8\right|\)
Tính:
e) \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{2}\)
f) \(\sqrt{6+\sqrt{11}}-\sqrt{6-\sqrt{11}}+3\sqrt{2}\)
