Question

Evaluate after rationalising the denominator (25/root 40 - root 80) given that root 5 =2.236 and root 10 = 3.162

Answer 1

Solution is attached below

Answer 2

Answer:

⇒ 1.193

Step-by-step explanation:

We have ,

$= > \frac{25}{ \sqrt{40} - \sqrt{80} } = \frac{25}{2 \sqrt{10} - 4 \sqrt{5} }$

$= > \frac{25}{2( \sqrt{10} - 2 \sqrt{5}) } \times \frac{( \sqrt{10} + 2 \sqrt{5} ) }{( \sqrt{10} + 2 \sqrt{5} )}$

$= > \frac{25( \sqrt{10} + 2 \sqrt{5}) }{2( \sqrt{10} - 2 \sqrt{5})( \sqrt{10} + 2 \sqrt{5}) }$

$= > \frac{25( \sqrt{10} + 2 \sqrt{5}) }{2((10)^{2} - (2 \sqrt{5})^{2} )}$

$= > \frac{25( \sqrt{10} + 2 \sqrt{5} ) }{2(100 - 20)}$

$= > \frac{25( \sqrt{10} + 2 \sqrt{5} )}{160}$

$= > \frac{5( \sqrt{10} + 2 \sqrt{5}) }{32}$

$= > \frac{5(3.162 - 2 \times 2.236)}{32}$

$= > \frac{5 \times 7.634}{32} = \frac{38.17}{32}$

⇒ 1.928 ≈ 1.193