\(\sqrt{16-2\sqrt{55}}=\sqrt{11}-\sqrt{5}\)

=>a=11; b=5

=>a-b=6

1)
\(=\sqrt{\left(\sqrt{11}\right)^2-2.\sqrt{11}.\sqrt{3}+\left(\sqrt{3}\right)^2}\)
\(=\sqrt{\left(\sqrt{11}-\sqrt{3}\right)^2}=\sqrt{11}-\sqrt{3}\)
2)
\(=\sqrt{\left(\sqrt{7}\right)^2-2.\sqrt{7}\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}=\sqrt{7}-\sqrt{5}\)
3)
\(=\sqrt{\left(\sqrt{11}\right)^2-2.\sqrt{11}\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(\sqrt{11}-\sqrt{5}\right)}=\sqrt{11}-\sqrt{5}\)
4)
\(=\sqrt{3^2-2.3.\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(3-\sqrt{5}\right)^2}=3-\sqrt{5}\)
5)
\(=\sqrt{3^2-2.3.2\sqrt{2}+\left(2\sqrt{2}\right)^2}=\sqrt{\left(3-2\sqrt{2}\right)^2}=3-2\sqrt{2}\)

 

\(\sqrt{a}-\sqrt{b}=\sqrt{16-2\sqrt{55}}=\sqrt{\left(\sqrt{11}-\sqrt{5}\right)^2}=\sqrt{11}-\sqrt{5}\Rightarrow a-b=6\)

\(\sqrt{16-2\sqrt{55}}=\sqrt{5-2\sqrt{5}\sqrt{11}+11}\) \(=\sqrt{\left(\sqrt{5}-\sqrt{11}\right)^2}=\sqrt{5}-\sqrt{11}\)

1,080556813

=1,080556813

a) Ta có: \(\sqrt{14-2\sqrt{33}}\)

\(=\sqrt{11-2\cdot\sqrt{11}\cdot\sqrt{3}+3}\)

\(=\sqrt{\left(\sqrt{11}-\sqrt{3}\right)^2}\)

\(=\left|\sqrt{11}-\sqrt{3}\right|\)

\(=\sqrt{11}-\sqrt{3}\)(Vì \(\sqrt{11}>\sqrt{3}\))

b) Ta có: \(\sqrt{12-2\sqrt{35}}\)

\(=\sqrt{7-2\cdot\sqrt{7}\cdot\sqrt{5}+5}\)

\(=\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}\)

\(=\left|\sqrt{7}-\sqrt{5}\right|\)

\(=\sqrt{7}-\sqrt{5}\)(Vì \(\sqrt{7}>\sqrt{5}\))

c) Ta có: \(\sqrt{16-2\sqrt{55}}\)

\(=\sqrt{11-2\cdot\sqrt{11}\cdot\sqrt{5}+5}\)

\(=\sqrt{\left(\sqrt{11}-\sqrt{5}\right)^2}\)

\(=\left|\sqrt{11}-\sqrt{5}\right|\)

\(=\sqrt{11}-\sqrt{5}\)(Vì \(\sqrt{11}>\sqrt{5}\))

d) Ta có: \(\sqrt{14-6\sqrt{5}}\)

\(=\sqrt{9-2\cdot3\cdot\sqrt{5}+5}\)

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

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

\(=3-\sqrt{5}\)(Vì \(3>\sqrt{5}\))

e) Ta có: \(\sqrt{17-12\sqrt{2}}\)

\(=\sqrt{9-2\cdot3\cdot2\sqrt{2}+8}\)

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

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

\(=3-2\sqrt{2}\)(Vì \(3>2\sqrt{2}\))

\(\sqrt{16-2\sqrt{55}}=\sqrt{\left(\sqrt{11}-\sqrt{5}\right)^2}=\sqrt{11}-\sqrt{5}\)

suy ra a=11;b=5

suy ra a+b=11+5=16

 a+b=16

Nếu \(\sqrt{16-2\sqrt{55}}=\) \(\sqrt{a}-\sqrt{b}\) với \(a,b\)\(EZ\)thì a + b = 16.

\(\sqrt{16-2\sqrt{55}}=\sqrt{\left(\sqrt{11}-\sqrt{5}\right)^2}\)

=\(\sqrt{11}-\sqrt{5}\)

=> a=11 và b=5

=> a-b=6

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