Question

Rút gọn biểu thức :

a) \(\sqrt{\left(4-\sqrt{15}\right)^2}\)+ \(\sqrt{15}\)

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

Answer 1

a) \(\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{15}=\left|4-\sqrt{15}\right|+\sqrt{15}=4-\sqrt{15}+\sqrt{15}=4\)

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

Answer 2

a) Ta có: \(\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{15}\)

\(=\left|4-\sqrt{15}\right|+\sqrt{15}\)

\(=4-\sqrt{15}+\sqrt{15}\)

=4

b) Ta có: \(\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(1-\sqrt{3}\right)^2}\)

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

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

\(=1\)

Answer 3

a) \(\sqrt{\left(4-\sqrt{15}\right)^{2^{ }}}+\sqrt{15}\)

=\(\left|4-\sqrt{15}\right|+\sqrt{15}\)

= \(4-\sqrt{15}+\sqrt{15}\) ( vì 4 =\(\sqrt{16}\) mà \(\sqrt{16}>\sqrt{15}\) )

=4

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

=\(\left|2-\sqrt{3}\right|+\left|1-\sqrt{3}\right|\) ( vì \(1< \sqrt{3}< 2\))

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

=1