\(\sqrt{\sqrt{5}-\sqrt{9-\sqrt{29+12\sqrt{5}}}}\)
K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

1 tháng 10 2021

\(\sqrt{13+30\sqrt{2}+\sqrt{9+4\sqrt{2}}}\)

\(=\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}\right)^2}+4\sqrt{2}+1^2}}\)

\(=\sqrt{13+30\sqrt{2+2\sqrt{2}+1^2}}\)

\(=\sqrt{13+30\sqrt{\left(\sqrt{2}\right)^2+2\sqrt{2}+1^2}}\)

\(=\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)

\(=\sqrt{5^2+2.5.3\sqrt{2}+\left(3+\sqrt{2}\right)^2}\)

\(=\sqrt{\left(5+3+\sqrt{2}\right)^2}\)

\(=\sqrt{\left(5+6\right)}=\sqrt{11}\)

\(=5+6=11\)

2 tháng 10 2021

a)=1
b)=\(3\sqrt{2}+5\)

27 tháng 7 2015

1. \(=\sqrt{5-\sqrt{\left(2\sqrt{3}+1\right)^2}}+\sqrt{3+\sqrt{\left(2\sqrt{3}+1\right)^2}}=\sqrt{5-2\sqrt{3}-1}+\sqrt{3+2\sqrt{3}+1}=\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}=\sqrt{3}-1+\sqrt{3}+1=2\sqrt{3}\)

21 tháng 6 2016

1/ \(\sqrt{5-\sqrt{13+4\sqrt{3}}}+\sqrt{3+\sqrt{13+4\sqrt{3}}}\)

\(=\sqrt{5-\left(1+\sqrt{12}\right)^2}+\sqrt{3+\left(1+\sqrt{12}\right)^2}\)

\(=\sqrt{5-\left|1+\sqrt{12}\right|}+\sqrt{3+\left|1+\sqrt{12}\right|}\)

\(=\sqrt{5-1-\sqrt{12}}+\sqrt{3+1+\sqrt{12}}\)

\(=\sqrt{4-\sqrt{12}}+\sqrt{4+\sqrt{12}}\)

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

\(=\left|\sqrt{3}-1\right|+\left|\sqrt{3}+1\right|\)

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

12 tháng 7 2019

\(A=\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)

\(=\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{\left(2-\sqrt{3}\right)^2}\)

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

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

\(=2\sqrt{3}\)

\(B=\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)

\(=\sqrt{\left(3+\sqrt{2}\right)^2}-\sqrt{\left(3-\sqrt{2}\right)^2}\)

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

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

\(=2\sqrt{2}\)

\(C=\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}\)

\(=\sqrt{\left(3+2\sqrt{2}\right)^2}+\sqrt{\left(3-2\sqrt{2}\right)^2}\)

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

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

\(=6\)

\(D=\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)

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

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

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

\(=4\)

\(E=\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)

\(=\sqrt{\left(1+\sqrt{5}\right)^2}-\sqrt{\left(1-\sqrt{5}\right)^2}\)

\(=|1+\sqrt{5}|-|1-\sqrt{5}|\)

\(=1+\sqrt{5}-\sqrt{5}+1\)

\(=2\)

12 tháng 7 2019

\(A=\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)

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

A = 2 + 2

A = 4

\(B=\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)

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

B = 3 + 3

B = 6

\(C=\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}\)

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

C = 3 + 3

C = 6

\(D=\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)

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

D = 2 + 2

D = 4

\(E=\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)

\(E=\sqrt{5}+1-\sqrt{5}+1\)

E = 1 + 1

E = 2

14 tháng 7 2019

\(\sqrt{24+8\sqrt{5}}+\) \(\sqrt{9-4\sqrt{5}}=\) \(\sqrt{\left(2\sqrt{5}\right)^2+2.2\sqrt{5}.2+4}\) + \(\sqrt{5-2\sqrt{5}.2+4}\)

\(\sqrt{\left(2\sqrt{5}+2\right)^2}+\) \(\sqrt{\left(\sqrt{5}-2\right)^2}\) = \(2\sqrt{5}+2+\sqrt{5}-2=3\sqrt{5}\)

==================================================

\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\) = \(\sqrt{\sqrt{5}-\sqrt{3-\left(2\sqrt{5}-3\right)}}\)\(\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}=\sqrt{\sqrt{5}-\sqrt{5}+1}=1\)

===========================================================

\(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}=\sqrt{13+30\sqrt{2+2\sqrt{2}+1}}\)

\(\sqrt{13+30\sqrt{3+2\sqrt{2}}}=\sqrt{13+30\left(\sqrt{2}+1\right)}=\sqrt{43+30\sqrt{2}}\) \(=\sqrt{\left(3\sqrt{2}+5\right)^2}=3\sqrt{2}+5\)

================================================================

6 tháng 6 2019

a) \(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)

\(=\sqrt{3}+1-\left(\sqrt{3}-1\right)\)

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

\(=2\)

b) \(\sqrt{9-4\sqrt{5}}-\sqrt{9+4\sqrt{5}}\)

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

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

\(=-4\)

6 tháng 6 2019

a) \(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)

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

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

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

\(=2\)

b) tương tự

6 tháng 6 2018

Cần lắm hông

6 tháng 6 2018

a/ \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)

\(=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(3-2\sqrt{5}\right)^2}}}\)

\(=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)

\(=\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}=1\)

b,c tương tự

7 tháng 7 2017

\(A=\left(2-\sqrt{3}\right)\sqrt{4+2.2.\sqrt{3}+3}=\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)=1\)

các câu còn lại làm tương tự nhé bạn !

19 tháng 8 2017

Hà Nam răng từ\(\sqrt{4}.....\)sang đc 2+ căn 3 đó ???