Question

simplefy 1/7+4 root 3+1/2+root 5

Answer 1

your answer is in attachment

Answer 2

$\displaystyle \sf{ \frac{1}{7 + 4 \sqrt{3} } + \frac{1}{2 + \sqrt{5} } }= 5 - 4 \sqrt{3} + \sqrt{5}$

Given : $\displaystyle \sf{ \frac{1}{7 + 4 \sqrt{3} } + \frac{1}{2 + \sqrt{5} } }$

To find : To simplify

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ \frac{1}{7 + 4 \sqrt{3} } + \frac{1}{2 + \sqrt{5} } }$

Step 2 of 2 :

Simplify the given expression

We simplify it as below

$\displaystyle \sf{ \frac{1}{7 + 4 \sqrt{3} } + \frac{1}{2 + \sqrt{5} } }$

$\displaystyle \sf{ = \frac{7 - 4 \sqrt{3} }{(7 + 4 \sqrt{3})(7 - 4 \sqrt{3} ) } + \frac{2 - \sqrt{5} }{(2 + \sqrt{5})(2 - \sqrt{5}) } }$

$\displaystyle \sf{ = \frac{7 - 4 \sqrt{3} }{ {7}^{2} - {(4 \sqrt{3}) }^{2} } + \frac{2 - \sqrt{5} }{ {2}^{2} - {( \sqrt{5} )}^{2} } }$

$\displaystyle \sf{ = \frac{7 - 4 \sqrt{3} }{ 49 - 48} + \frac{2 - \sqrt{5} }{ 4 - 5} }$

$\displaystyle \sf{ = \frac{7 - 4 \sqrt{3} }{ 1} + \frac{2 - \sqrt{5} }{ - 1} }$

$\displaystyle \sf{ = 7 - 4 \sqrt{3} - 2 + \sqrt{5} }$

$\displaystyle \sf{ = 5 - 4 \sqrt{3} + \sqrt{5} }$

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