Question

hey brainly users i want fast answer to my question. ❌❌ spammers plzz stay away❌❌ the answer is -1.466 but i want full solution ​

Answer 1

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

We see , we are given the values of √2 and √6 . And we need to find a value of fraction which has √3 as one of the terms of denominator . So firstly by substituting the values, we will find the value of √3 . Then we will apply it in denominator and find the answer .

Let's do it !!

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★ To Find :-

$\\\;\large{\bf{\pink{\mapsto\;\;\;\dfrac{1}{\sqrt{3}\;-\;\sqrt{2}\;-\;1}}}}$

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★ Solution :-

Given,

» Value of √2 = 1.4142

» Value of √6 = 2.4495

____________________________________________

~ For the value of √3 ::

We know that,

$\\\;\sf{:\rightarrow\;\;\orange{\sqrt{6\:}\;=\;\bf{2.4495}}}$

• Since, √2 × √3 = √6 . This can be written as,

$\\\;\sf{:\leadsto\;\;\sqrt{2\:}\;\times\;\sqrt{3\:}\;=\;\bf{2.4495}}$

• And, √2 = 1.4142

By applying this value, we get,

$\\\;\sf{:\leadsto\;\;1.4142\;\times\;\sqrt{3\:}\;=\;\bf{2.4495}}$

$\\\;\sf{:\leadsto\;\;\sqrt{3\:}\;=\;\bf{\dfrac{2.4495}{1.4142}}}$

$\\\;\bf{:\leadsto\;\;\sqrt{3\:}\;=\;\bf{\red{1.7321}}}$

____________________________________________

~ For the required answer ::

Now we already have the required values. Let's find the answer.

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{\sqrt{3}\;-\;\sqrt{2}\;-\;1}}$

On applying the values, we get

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{1.7321\;-\;1.4142\;-\;1}}$

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{1.7321\;-\;1.4142\;-\;1}}$

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{0.3179\;-\;1}}$

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{\;-\;0.6821}}$

On changing the sign,

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{\;-\;0.6821}\;\times\;\dfrac{-\:1}{-\:1}}$

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1\;\times\;(-1)}{\;-\;0.6821\;\times\;(-1)}}$

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{\;-\;0.6821}}$

$\\\;\bf{\Longrightarrow\;\;\;-\;1.4661}$

• Since here the digits after decimal are 4 and we need to find the answer till 3 digits. So let's round off the digits.

$\\\;\bf{\blue{\Longrightarrow\;\;\;-\;1.466}}$

$\\\;\large{\underline{\boxed{\tt{Hence,\;\;required\;\;answer\;=\;\bf{\purple{-\;1.466}}}}}}$

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★ More to know :-

• Some exponential formulae ::

$\\\;\tt{\leadsto\;\;a^{1/2}\;=\;\sqrt{a}}$

$\\\;\tt{\leadsto\;\;a^{-\:1}\;=\;\dfrac{1}{a}}$

$\\\;\tt{\leadsto\;\;(a^{m})^{n}\;=\;a^{mn}}$

$\\\;\tt{\leadsto\;\;a^{m}\;+\;a^{n}\;=\;a^{m\;+\;n}}$

$\\\;\tt{\leadsto\;\;a^{0}\;=\;1}$

$\\\;\tt{\leadsto\;\;a^{1}\;=\;a}$

• Some algebraic identities ::

$\\\;\tt{\leadsto\;\;(a\;+\;b)^{2}\;=\;a^{2}\;+\;b^{2}\;+\;2ab}$

$\\\;\tt{\leadsto\;\;(a\;-\;b)^{2}\;=\;a^{2}\;+\;b^{2}\;-\;2ab}$

$\\\;\tt{\leadsto\;\;(a\;-\;b)(a\;+\;b)\;=\;a^{2}\;-\;b^{2}}$

$\\\;\tt{\leadsto\;\;(a\;+\;b\;+\;c)^{2}\;=\;a^{2}\;+\;b^{2}\;+\;c^{2}\;+\;2ab\;+\;2ac\;+\;2bc}$

$\\\;\tt{\leadsto\;\;a^{2}\;+\;b^{2}\;=\;(a\;+\;b)^{2}\;-\;2ab}$

Answer 2

$\large\bold\green{\checkmark{Verified~Answer}}$

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

We see , we are given the values of √2 and √6 . And we need to find a value of fraction which has √3 as one of the terms of denominator . So firstly by substituting the values, we will find the value of √3 . Then we will apply it in denominator and find the answer .

Let's do it !!

____________________________________________

★ To Find :-

$\\\;\large{\bf{\red{\mapsto\;\;\;\dfrac{1}{\sqrt{3}\;-\;\sqrt{2}\;-\;1}}}}$

____________________________________________

★ Solution :-

Given,

» Value of √2 = 1.4142

» Value of √6 = 2.4495

____________________________________________

~ For the value of √3 ::

We know that,

$\\\;\sf{:\rightarrow\;\;\purple{\sqrt{6\:}\;=\;\bf{2.4495}}}$

• Since, √2 × √3 = √6 . This can be written as,

$\\\;\sf{:\leadsto\;\;\sqrt{2\:}\;\times\;\sqrt{3\:}\;=\;\bf{2.4495}}$

• And, √2 = 1.4142

By applying this value, we get,

$\\\;\sf{:\leadsto\;\;1.4142\;\times\;\sqrt{3\:}\;=\;\bf{2.4495}}$

$\\\;\sf{:\leadsto\;\;\sqrt{3\:}\;=\;\bf{\dfrac{2.4495}{1.4142}}}$

$\\\;\bf{:\leadsto\;\;\sqrt{3\:}\;=\;\bf{\red{1.7321}}}$

____________________________________________

~ For the required answer ::

Now we already have the required values. Let's find the answer.

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{\sqrt{3}\;-\;\sqrt{2}\;-\;1}}$

On applying the values, we get

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{1.7321\;-\;1.4142\;-\;1}}$

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{1.7321\;-\;1.4142\;-\;1}}$

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{0.3179\;-\;1}}$

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{\;-\;0.6821}}$

On changing the sign,

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{\;-\;0.6821}\;\times\;\dfrac{-\:1}{-\:1}}$

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1\;\times\;(-1)}{\;-\;0.6821\;\times\;(-1)}}$

$\\\;\bf{\Longrightarrow\;\;\;\dfrac{1}{\;-\;0.6821}}$

$\\\;\bf{\Longrightarrow\;\;\;-\;1.4661}$

• Since here the digits after decimal are 4 and we need to find the answer till 3 digits. So let's round off the digits.

$\\\;\bf{\blue{\Longrightarrow\;\;\;-\;1.466}}$

$\\\;\large{\underline{\boxed{\tt{Hence,\;\;required\;\;answer\;=\;\bf{\orange{-\;1.466}}}}}}$

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