√(11 - 6 √(2)) (not decimal form)

Mathematics

1 answer:

bogdanovich [222]3 years ago

6 0

Answer:

$\huge\boxed{\sqrt{11-6\sqrt2}=3-\sqrt2}$

Step-by-step explanation:

$\sqrt{11-6\sqrt2}=(*)\\\\11=9+2=3^2+(\sqrt2)^2\\6\sqrt2=(2)(3)(\sqrt2)\\\\(*)=\sqrt{3^2-(2)(3)(\sqrt2)+(\sqrt2)^2}\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=\sqrt{(3-\sqrt2)^2}\\\\\text{use}\ \sqrt{a^2}=|a|\\\\=|3-\sqrt2|=3-\sqrt2\\\\^{\text{because}\ 3>\sqrt2\to3-\sqrt2>0}$

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