Question

express 3 upon 7 + 2 root 5, with rational denominator

Answer 1

3/7+2root5
=3(7-2root5)/(7+2root5)(7-2root5)
=21-6root5/7^2-(2root5)^2
=21-6root5/49-20
=21-6root5/29

Answer 2

Answer:

Concept :

Rationalizing the denominator is the process of shifting a root, such as a square root or a cube root, from the fraction's denominator to its numerator. In doing so, we reduce the fraction to its most basic form, which makes the denominator rational. Unfair Denominator.

Explanation:

Given :

$\frac{3}{7}$ + $\frac{2}{\sqrt{5} }$

To find :

Rational denominator

Solution :

 $\frac{3}{ 7+2\sqrt{5} }$     ×     $\frac{7-2\sqrt{5} }{7-2\sqrt{5}}$

we know that ,

(a+b) (a-b )= $a^{2} - b^{2}$

=    $\frac{21 - 6\sqrt{5} }{7^{2} - (2\sqrt{5})^{2} }$  

= $\frac{21 - 6\sqrt{5} }{49 - 20 }$

= $\frac{21 - 6\sqrt{5} }{29}$

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