Question

0.8 Rationalize the denominator of
X=1/7+4√3​

Answer 1

Answer:

$= > 7 - 4 \sqrt{3}$

Step-by-step explanation:

$Since, \:the \: denominator = 7 + 4 \sqrt{3} , \\ it's \: rationalising \: factor \\ = 7 - 4 \sqrt{3} \\ Therefore, \\ \frac{1}{7 + 4 \sqrt{3} } = \frac{1}{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ = \frac{7 - 4 \sqrt{3} }{49 - 48} \\ Since, \\ [(7 + 4 \sqrt{3} )(7 - 4 \sqrt{3}) = (7) {}^{2} - (4 \sqrt{3} ) {}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 49 - 48 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1] \\ </p><p> = > 7 - 4 \sqrt{3}$

Answer 2

Answer:

7-4√3

Step-by-step explanation:

multiply both denominator and numerator by (7-4√3) so that we can use the identity

(a+b)(a-b) = a²-b²

=> (7-4√3)/[(7+4√3)(7-4√3)]

=> (7-4√3)/(7² - (4√3)²)

=> (7-4√3)/(49 - 48)

=> (7-4√3)/ 1

=> 7-4√3