wholeroot14×root5-80
Answers
Answer:
Answer:
\frac{15}{\sqrt{10}+\sqrt{20}+\sqrt{40}-\sqrt{5}-\sqrt{80}}=5.398
10
+
20
+
40
−
5
−
80
15
=5.398
Step-by-step explanation:
\begin{gathered} Given \\\sqrt{5}=2.236,\:\sqrt{10}=3.162\end{gathered}
Given
5
=2.236,
10
=3.162
i)\sqrt{10}--(1)i)
10
−−(1)
ii)\sqrt{20}=\sqrt{2^{2}\times 5}=2\sqrt{5}--(2)ii)
20
=
2
2
×5
=2
5
−−(2)
iii)\sqrt{5}--(3)iii)
5
−−(3)
iv)\sqrt{40}=\sqrt{2^{2}\times 10}=2\sqrt{10}--(4)iv)
40
=
2
2
×10
=2
10
−−(4)
v)\sqrt{80}=\sqrt{4^{2}\times 5}=4\times 5--(5)v)
80
=
4
2
×5
=4×5−−(5)
\begin{gathered}Now,\\\frac{15}{\sqrt{10}+\sqrt{20}+\sqrt{40}-\sqrt{5}-\sqrt{80}}\\=\frac{15}{\sqrt{10}+2\sqrt{5}+2\sqrt{10}-\sqrt{5}-4\sqrt{5}}\\=\frac{15}{3\sqrt{10}-3\sqrt{5}}\\=\frac{15}{3(\sqrt{10}-\sqrt{5})}\end{gathered}
Now,
10
+
20
+
40
−
5
−
80
15
=
10
+2
5
+2
10
−
5
−4
5
15
=
3
10
−3
5
15
=
3(
10
−
5
)
15
/* Rationalising the denominator, we get
\begin{gathered}=\frac{15(\sqrt{10}+\sqrt{5}}{3(\sqrt{10}-\sqrt{5})(\sqrt{10}+\sqrt{5})}\\=\frac{15(\sqrt{10}+\sqrt{5}}{3[(\sqrt{10})^{2}-(\sqrt{5})^{2}]}\\=\frac{15(\sqrt{10}+\sqrt{5}}{3(10-5)}\\=\frac{15(\sqrt{10}+\sqrt{5})}{3\times 5 }\\=\frac{15(\sqrt{10}+\sqrt{5})}{15}\\=\sqrt{10}+\sqrt{5}\\=3.162+2.236\\=5.398\end{gathered}
=
3(
10
−
5
)(
10
+
5
)
15(
10
+
5
=
3[(
10
)
2
−(
5
)
2
]
15(
10
+
5
=
3(10−5)
15(
10
+
5
=
3×5
15(
10
+
5
)
=
15
15(
10
+
5
)
=
10
+
5
=3.162+2.236
=5.398
Therefore,
\frac{15}{\sqrt{10}+\sqrt{20}+\sqrt{40}-\sqrt{5}-\sqrt{80}}=5.398
10
+
20
+
40
−
5
−
80
15
=5.398
•••♪
Step-by-step explanation:
- please make it a brainliest answer.