Math, asked by Abhiramnivas, 1 month ago

wholeroot14×root5-80​

Answers

Answered by Anonymous
7

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:

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