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Maths-

General

Easy

Question

Simplify by rationalizing: $fraction numerator 7 plus 3 square root of 5 over denominator 7 minus 3 square root of 5 end fraction$

hint Hint:

Hint:
Rationalization is a technique which is used to eliminate the irrational number in the denominator. For example, $fraction numerator 1 over denominator square root of 3 end fraction$ can be rationalised as $fraction numerator 1 over denominator square root of 3 end fraction cross times fraction numerator square root of 3 over denominator square root of 3 end fraction equals fraction numerator square root of 3 over denominator 3 end fraction$

The correct answer is: 47/2+21/2 √5 .

Let’s say x = $fraction numerator 7 plus 3 square root of 5 over denominator 7 minus 3 square root of 5 end fraction$
To rationalise the denominator, we can multiply $7 plus 3 square root of 5$ to the numerator and denominator.
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals fraction numerator 7 plus 3 square root of 5 over denominator 7 minus 3 square root of 5 end fraction cross times fraction numerator 7 plus 3 square root of 5 over denominator 7 plus 3 square root of 5 end fraction end cell row cell x equals fraction numerator left parenthesis 7 plus 3 square root of 5 right parenthesis squared over denominator 7 squared minus left parenthesis 3 square root of 5 right parenthesis squared end fraction end cell row cell x equals fraction numerator 49 plus 45 plus 2 cross times 7 cross times 3 square root of 5 over denominator 49 minus 45 end fraction end cell row cell x equals fraction numerator 94 plus 42 square root of 5 over denominator 4 end fraction end cell row cell x equals 94 over 4 plus 42 over 4 square root of 5 end cell row cell x equals 47 over 2 plus 21 over 2 square root of 5 end cell end table$
Final Answer:
Hence, the simplified value of $fraction numerator 7 plus 3 square root of 5 over denominator 7 minus 3 square root of 5 end fraction$ is $47 over 2 plus 21 over 2 square root of 5$

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