Question

Rationalile the denominator of
1|√2+3​

Answer 1

Answer:

1/√2+3

= 1 / √2+3 × √2-3 / √2-3

= √2-3 / (√2)^2 - (3)^2

= √2-3 / 2 - 9

= √2-3 / -7

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

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$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to rationalize the denominator$\large{\sf{\frac{1}{\sqrt{2} + 3}}}$

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$\Large{\underline{\underline{\bf{Explanation :}}}}$

For, rationalisation we will multiply the denominator in numerator and as well as denominator by changing the last sign.

$\sf{\mapsto \frac{1}{\sqrt{2} + 3}} \\ \\ \sf{\mapsto \frac{1}{\sqrt{2} + 3} \times \frac{\sqrt{2} - 3}{\sqrt{2} - 3}}$

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$\Large{\star{\boxed{\sf{(a + b)(a - b) = a^2 - b^2}}}}$

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$\sf{\mapsto \frac{ \sqrt{2} - 3}{(\sqrt{2})^2 - (3)^2}} \\ \\ \sf{\mapsto \frac{ \sqrt{2} - 3}{2 - 9} } \\ \\ \sf{\mapsto \frac{ \sqrt{2} - 3}{-7} }$