Question

Simplify each of the following by rationalising the denominator (i) 7+3√5÷ 7-3√5​

Answer 1

EXPLANATION

Rationalize the equation

7 + 3√5 / 7 - 3√5

7 + 3√5 / 7 - 3√5 X 7 + 3√5 / 7 + 3√5

( 7 + 3√5 ) ^2 / 49 - 45

49 + 45 + 42√5 / 4

94 + 42√5 / 4

2(47 + 21√5 ) / 4

47 + 21√5 / 2 = ANSWER

Answer 2

⠀⠀⠀⠀⠀⠀⠀⠀$\bf \frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } \\ \\ \bf \frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } \times \bf \frac{7 + 3 \sqrt{5} }{7 + 3 \sqrt{5} } \\ \\ \bf \frac{(7 + 3 \sqrt{5} )^{2} }{(7)^{2} - (3 \sqrt{5} )^{2} } \\ \\ \bf \frac{49 + 45 + 42 \sqrt{5} }{49- 45 } \\ \\ \bf \frac{94+ 42\sqrt{5} }{4} \\ \\ \bf \frac{47+ 21\sqrt{5} }{2}$