Question

1) √(27 + 10 × √2) + √(11 – 6 × √2)
2) 2 × √(7 – 4 × √3) + √(13 – 4 × √3)
по действиям пожалуйста и с обьяснением

Answer 1

1)

√(27+10√2)+√(11-6√2)=√(25+2*5*√2+2)+√(9-2*3*√2+2)=

=√(5²+2*5*√2+(√2)√+√(3²-2*3*√2+(√2)²)=√(5+√2)²+√(3-√2)²=5+√2+3-√2=8.

2)

2*√(7-4*√3)+√(11-4√3)=2*√(4-2*2*√3+3)+√(1-4*√3+12)=

=2*√(2²-2*2*√3+(√3)²)+√(1²-2*1*2√3+(2√3)²=2*√(2-√3)²+√(1-2√3)²=

2*(2-√3)+|1-2√3|=4-2√3+2√3-1=3.

Answer 2

$\displaystyle \tt 1) \ \ \sqrt{27+10\sqrt{2}} +\sqrt{11-6\sqrt{2}} = \\\\ =\sqrt{25+10\sqrt{2}+2} +\sqrt{9-6\sqrt{2}+2} = \sqrt{(5+\sqrt{2})^2} +\sqrt{(3-\sqrt{2})^2} = \\\\ = 5+\sqrt{2}+3-\sqrt{2}=8$

$\displaystyle \tt 2) \ \ 2\sqrt{7-4\sqrt{3}} +\sqrt{13-4\sqrt{3}} = \\\\ 2\sqrt{4-4\sqrt{3}+3} +\sqrt{1-4\sqrt{3}+12}=2\sqrt{(2-\sqrt{3})^2} +\sqrt{(1-2\sqrt{3})^2}= \\\\=2(2-\sqrt{3})+|1-2\sqrt{3}| =4-2\sqrt{3}+2\sqrt{3}-1 = 3$