Question

Rationalize 1 upon root 7 minus 6

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

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To Find :

$\sf{ we \: \: have \: \: to \: \: rationalize \: \frac{1}{ \sqrt{7} - 6 } }$

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Solution :

Note :- When we rationalize a number firstly we have to change the sign of the denominator and then we have to multiply it by both numerator and denominator.

We can use rationalize method only when there is root in the denominator.

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Now, we are changing the sign and multiplying them.

$\sf{ \implies \: \frac{1}{ \sqrt{7} - 6 } } \\ \\ \sf{ \implies \: \frac{1}{ \sqrt{7} - 6} \times \frac{ \sqrt{7} + 6 }{ \sqrt{7} + 6 } } \\ \\ \star \underline{\boxed{\sf{(a - b)(a + b) = {a}^{2} - {b}^{2}}}} \\ \\ \sf{ \implies \frac{ \sqrt{7} + 6 }{ {\cancel{\sqrt{(7)}^{2}} - ( {6)}^{2} } } } \\ \\ \sf{ \implies \frac{ \sqrt{7} + 6}{7 - 36} } \\ \\ \sf{ \implies \frac{ \sqrt{7} + 6 }{ - 29} } \\ \\ \sf{ \implies\frac{ - (\sqrt{7} + 6) }{29} }$

$\Large \hookrightarrow {\underline{\boxed{\sf{\frac{-(\sqrt{7} + 6)}{29}}}}}$

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#BAL

Answer 2

$\large{\underline{\underline{\mathfrak{\red{\sf{Answer-}}}}}}$

$\bold{\green{\sf{\dfrac{-(\sqrt7-6)}{29}}}}$

$\large{\underline{\underline{\mathfrak{\red{\sf{Explanation-}}}}}}$

$\bold{\sf{\dfrac{1}{\sqrt7-6}}}$

Rationalising the denominator,

= $\bold{\sf{\dfrac{1}{\sqrt7-6}}}$ × $\bold{\sf{\dfrac{\sqrt7+6}{\sqrt7+6}}}$

Now, we know that,

$\large{\boxed{\sf{\underline{(a^2-b^2=(a+b)(a-b)}}}}$

= $\bold{\sf{\dfrac{\sqrt7+6}{\cancel{\sqrt7^2}-6^2}}}$ ( cancelling square and square root )

= $\bold{\sf{\dfrac{\sqrt7+6}{7-36}}}$

= $\bold{\sf{\dfrac{\sqrt7+6}{-29}}}$

= $\bold{\green{\sf{\dfrac{-(\sqrt7-6)}{29}}}}$

★Note :

• We can Rationalization method to remove the root from the denominator.

• While solving these types of questions, you have to multiply and divide the denominator of given digit.