Simplify:
(Root 5 + Root 3) / (Root 80 + Root 48 - Root 27 - Root 45)
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0
Answer:
1
Step-by-step explanation:
Given expression,
\frac{\sqrt{5}+\sqrt{3}}{\sqrt{80}+\sqrt{48}-\sqrt{45}-\sqrt{27}}
80
+
48
−
45
−
27
5
+
3
=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{16\times 5}+\sqrt{16\times 3}-\sqrt{9\times 5}-\sqrt{9\times 3}}=
16×5
+
16×3
−
9×5
−
9×3
5
+
3
=\frac{\sqrt{5}+\sqrt{3}}{4\sqrt{5}+4\sqrt{3}-3\sqrt{5}-3\sqrt{3}}=
4
5
+4
3
−3
5
−3
3
5
+
3
(\because \sqrt{a\times b}=\sqrt{a}\times \sqrt{b})(∵
a×b
=
a
×
b
)
=\frac{\sqrt{5}+\sqrt{3}}{4(\sqrt{5}+\sqrt{3})-3(\sqrt{5}+\sqrt{3})}=
4(
5
+
3
)−3(
5
+
3
)
5
+
3
=\frac{\sqrt{5}+\sqrt{3}}{(\sqrt{5}+\sqrt{3})(4-3)}=
(
5
+
3
)(4−3)
5
+
3
=1=1
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