Question

\(a.\sqrt{7+4\sqrt{3}}.\sqrt{7-4\sqrt{3}}\)

\(b.\sqrt{57+28\sqrt{2}}\)

\(c.\sqrt{5}-\sqrt{9-4\sqrt{5}}\)

\(d.\left(2+\sqrt{3}\right)\sqrt{7-4\sqrt{3}}\)

Answer 1

a, \(\sqrt{7+4\sqrt{3}}.\sqrt{7-4\sqrt{3}}\)

=\(\sqrt{2^2+2.2.\sqrt{3}+\left(\sqrt{3}\right)^2}.\sqrt{2^2-2.2.\sqrt{3}+\left(\sqrt{3}\right)^2}.\)

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

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

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

= 4-3

=1

Answer 2

mấy câu còn lại tại mỏi tay quá nên k làm, bạn thông cảm

Answer 3

a) \(\sqrt{7+4\sqrt{3}}.\sqrt{7-4\sqrt{3}}=\sqrt{\left(7+4\sqrt{3}\right)\left(7-4\sqrt{3}\right)}=\sqrt{7^2-\left(4\sqrt{3}\right)^2}=\sqrt{49-48}=\sqrt{1}=1\)b) \(\sqrt{57+28\sqrt{2}}=\sqrt{49+2.7.2\sqrt{2}+8}=\sqrt{7^2+2.7.4\sqrt{2}+\left(2\sqrt{2}^2\right)}=\sqrt{\left(7+2\sqrt{2}\right)^2}=7+2\sqrt{2}\)

c) \(\sqrt{5}-\sqrt{9-4\sqrt{5}}=\sqrt{5}-\sqrt{5-2.\sqrt{5}.2+4}=\sqrt{5}-\sqrt{\left(\sqrt{5}-2\right)^2}=\sqrt{5}-\left|\sqrt{5}-2\right|=\sqrt{5}-\sqrt{5}+2=2\)

d) \(\left(2+\sqrt{3}\right)\sqrt{7-4\sqrt{3}}=\left(2+\sqrt{3}\right)\sqrt{4-2.2.\sqrt{3}+3}=\left(2+\sqrt{3}\right)\sqrt{\left(2-\sqrt{3}\right)^2}=\left(2+\sqrt{3}\right)\left|2-\sqrt{3}\right|=\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)=4-3=1\)