Đáp án:
Bài 2.
a, $\sqrt{(3-\sqrt{2})^{2}}$ = | 3 - $\sqrt{2}$ | = 3 - $\sqrt{2}$
b, $\sqrt{(\sqrt{11}+3)^{2}}$ =$\sqrt{11}$ + 3
c, $\sqrt{4-2\sqrt{3}}$ = $\sqrt{3-2\sqrt{3} + 1}$ = $\sqrt{(\sqrt{3}-1)^{2}}$ = | $\sqrt{3}$ - 1 | = $\sqrt{3}$ - 1
d, $\sqrt{7 + 4\sqrt{3}}$ = $\sqrt{4 + 4\sqrt{3} + 3 }$ = $\sqrt{(2 + \sqrt{3})^{2} }$ = 2 + $\sqrt{3}$
Bài 2B
a, $\sqrt{(2+\sqrt{3})^{2}}$ = 2 + $\sqrt{3}$
b, $\sqrt{(\sqrt{7}+3)^{2}}$ = $\sqrt{7}$ + 3
c, $\sqrt{6-2\sqrt{5}}$ = $\sqrt{5-2\sqrt{5} + 1}$ = $\sqrt{(\sqrt{5}-1)^{2}}$ = | $\sqrt{5}$ - 1 | = $\sqrt{5}$ - 1
d, $\sqrt{8 + 2\sqrt{7}}$ = $\sqrt{7 + 2\sqrt{7} + 1 }$ = $\sqrt{( \sqrt{7}+1)^{2} }$ = $\sqrt{7}$ + 1
Bài 3a.
a, $\sqrt{196}$ - $\sqrt{25}$ - 5$\sqrt{81}$
= 14 - 5 - 5.9
= 9 - 45
= -36
b, (32 : $\sqrt{16}$ + $\sqrt{289}$ ).$\sqrt{49}$
= ( 32 : 4 + 17 ). 7
= (8 + 17). 7
= 25 . 7
=175
c, $\sqrt{(10-3)^{2}}$ - $\sqrt{10}$
= $\sqrt{7^{2}}$ - $\sqrt{10}$
= 7 - $\sqrt{10}$
d, $\sqrt{(5 + \sqrt{7} )^{2}}$ - $\sqrt{8 - 2\sqrt{7}}$
= 5 + $\sqrt{7}$ - $\sqrt{7 - 2\sqrt{7} + 1}$
= 5 + $\sqrt{7}$ - $\sqrt{( \sqrt{7} - 1 )^{2}}$
= 5 + $\sqrt{7}$ - ( $\sqrt{7}$ - 1)
= 5 + $\sqrt{7}$ - $\sqrt{7}$ + 1
= 6
Bài 3b .
a, $\sqrt{64}$ . $\sqrt{25}$ + 10$\sqrt{36}$
= 8 . 5 + 10 . 6
=40 + 60
=100
b, (81. $\sqrt{97}$ + $\sqrt{169}$ ).$\sqrt{225}$
= (81.$\sqrt{97}$ + 13 ).15
= 1215$\sqrt{97}$ + 195
c, $\sqrt{(\sqrt{7}-1)^{2}}$ - $\sqrt{7}$
= | $\sqrt{7}$ - 1 | - $\sqrt{7}$
= $\sqrt{7}$ - 1 - $\sqrt{7}$
= -1
d, $\sqrt{(\sqrt{3}+1)^{2}}$ - $\sqrt{4-2\sqrt{3}}$
= $\sqrt{3}$ + 1 - $\sqrt{3-2\sqrt{3}+1}$
= $\sqrt{3}$ + 1 - $\sqrt{(\sqrt{3}-1)^{2}}$
= $\sqrt{3}$ + 1 - ( $\sqrt{3}$ - 1)
= $\sqrt{3}$ + 1 - $\sqrt{3}$ + 1
= 2
