Réponse:
(5
8−2
10
)(
2−
32
)
1 Factor out the common term 22.
5\sqrt{2(4-\sqrt{10})}\sqrt{2-\sqrt{32}}
5
2(4−
10
)
2−
32
2 Simplify \sqrt{32}
32
to 4\sqrt{2}4
2
.
5\sqrt{2(4-\sqrt{10})}\sqrt{2-4\sqrt{2}}
5
2(4−
10
)
2−4
2
3 Factor out the common term 22.
5\sqrt{2(4-\sqrt{10})}\sqrt{2(1-2\sqrt{2})}
5
2(4−
10
)
2(1−2
2
)
4 Simplify.
5\sqrt{2(4-\sqrt{10})\times 2(1-2\sqrt{2})}
5
2(4−
10
)×2(1−2
2
)
5 Simplify 2(4-\sqrt{10})\times 2(1-2\sqrt{2})2(4−
10
)×2(1−2
2
) to 4(4-\sqrt{10})(1-2\sqrt{2})4(4−
10
)(1−2
2
).
5\sqrt{4(4-\sqrt{10})(1-2\sqrt{2})}
5
4(4−
10
)(1−2
2
)
6 Use this rule: \sqrt{ab}=\sqrt{a}\sqrt{b}
ab
=
a
b
.
5\sqrt{4}\sqrt{(4-\sqrt{10})(1-2\sqrt{2})}
5
4
(4−
10
)(1−2
2
)
7 Since 2\times 2=42×2=4, the square root of 44 is 22.
5\times 2\sqrt{(4-\sqrt{10})(1-2\sqrt{2})}
5×2
(4−
10
)(1−2
2
)
