Respuesta :
C
given 1 /( 3 + √2 )
then rationalise the denominator by multiplying the numerator/ denominator by the conjugate of the denominator
the conjugate of 3 + √2 is 3 - √2
1 / (3 + √2 ) × (3 - √2 ) / (3 - √2 )
= (3 - √2 ) /( 9 - 2 ) = (3 - √2 ) / 7
The fraction [tex]\frac{1}{3+\sqrt{2}}[/tex] can be written as [tex]\frac{3-\sqrt 2}{7}[/tex]. Option C is correct.
What is a fraction simplification?
Fraction simplification is a method of fraction reduction that entails making a fraction as simple as possible.
This is accomplished by dividing the numerator and denominator by the biggest integer that divides both integers exactly.
Given fraction;
[tex]\frac{1}{3+\sqrt{2}}[/tex]
Multiplying the numerator and denominator by the conjugate of the denominator will rationalize the denominator;
The conjugate of the denominator (3 + √2) is 3 - √2;
Apply the rationalization of fraction;
[tex]\frac{1}{3+\sqrt{2}} \\\ \frac{1}{3+\sqrt{2}} \times \frac{3-\sqrt2}{3-\sqrt 2} \\\\ \frac{3-\sqrt 2}{9-2} \\\\\ \frac{3-\sqrt 2}{7}[/tex]
Hence option C is correct.
To learn more about fraction simplification, refer to https://brainly.com/question/11479469.
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