Question

Rationalize the denominator of
1/2+5√7​

Answer 1

Step-by-step explanation:

Rationalizing

$1 \div 2 + 5 \sqrt{7} \\ = 1 \div 2 + 5 \sqrt{7} \times 2 - 5 \sqrt{7} \div 2 - 5 \sqrt{7} \\ = 2 - 5 \sqrt{7} \div {2}^{2} - {5 \sqrt{7} }^{2} \\ = 2 - 5 \sqrt{7} \div 4 - 175 \\ = 2 - 5 \sqrt{7} \div ( - 171) \\ = - (2 - 5 \sqrt{7} ) \div 171 \\ = 5 \sqrt{7 } - 2 \div 171$

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Answer 2

1/(2+5√7)

=(1/(2+5√7))×((2-5√7)/(2-5√7)

=(2-5√7)/((2^2)-(5√7)^2)

=(2-5√7)/(4-(25×7))

=(2-5√7)/(4-175)

=(2-5√7)/(-171)

=(5√7-2)/171

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