Question

Rationalize the denominator:B%202%7D%20%20%7D%20" id="TexFormula1" title=" \frac{1}{ \sqrt{3} - \sqrt{ 2} } " alt=" \frac{1}{ \sqrt{3} - \sqrt{ 2} } " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

√3 + √2

Step-by-step explanation:

The best approach to this problem would be by multiplying the denominator ad numerator by the denominator's conjugate;

1(√3 + √2) / (√3 - √2)(√3 + √2)

= (√3 + √2) / (√3)^2 - (√2)^2

= √3 + √2 / 3 - 2

= √3 + √2 / 1 = √3 + √2

We now have a denominator of 1, which is rationalized. The solution would be √3 + √2.

Answer 2

Answer:

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$step\:1$

$\frac{1}{ \sqrt{3} - \sqrt{2} }$

write the equation

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$step\:2$

$\frac{1 \times ( \sqrt{3} + \sqrt{2}) }{ (\sqrt{3} - \sqrt{2} ) \times (\sqrt{3} + \sqrt{2}) }$

multiply both numerator and denominator by √3+√2

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$step\:3$

$\frac{ \sqrt{3} + \sqrt{2} }{ ( 3 ) - ( 2 ) }$

after multiplying numerator with √3+√2 we get→√3+√2

after multiplying denominator we get 3-2

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$step\:4$

$\frac{ \sqrt{3} + \sqrt{2} }{1}$

after subtracting 3 with 2 we get →1

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hence denominater is rationalized✓

hope it helped you:)