Question

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Answer 1

Answer:

27.03 / 17

Step-by-step explanation:

2√8 / 2√5-√3

= 2√8 / 2√5-√3 × 2√5+√3 / 2√5+√3

= 27.03 / (2√5)² - (√3)²

= 27.03 / (4×5) - (3)

= 27.03 / 20 - 3

= 27.03 / 17

Answer 2

$\sf given : - \frac{2 \sqrt{8} }{2 \sqrt{5} - \sqrt{3} } \\ \\ \sf = \frac{2 \sqrt{8} }{2 \sqrt{5} - \sqrt{3} } \times \frac{2 \sqrt{5} + \sqrt{3} }{2 \sqrt{5} + \sqrt{3} } \\ \\ \sf = \frac{2 \sqrt{8}(2 \sqrt{5} + \sqrt{3}) }{(2 \sqrt{5} - \sqrt{3})(2 \sqrt{5} + \sqrt{3} )} \\ \\ \sf = \frac{2 \sqrt{40} + 2 \sqrt{24} }{( {2 \sqrt{5} })^{2} - ( { \sqrt{3}) }^{2} } \\ \\ \sf = \frac{4 \sqrt{10} + 4 \sqrt{6} }{20 - 3} \\ \\ \sf = \boxed{ \frac{4 \sqrt{10} + 4 \sqrt{6} }{17} }$

identity used in the second step for the denominator is (a + b) (a - b) = a² - b²

also u might get confused in the 5th step.

actually

√40 = 2√10

➡ 2√40 = 2 × 2√10 = 4√10

√24 = 2√6

➡ 2√24 = 2 × 2√6 = 4√6