Question

2 root 8 upon 2 root 5 - root 3

Answer 1

Given: 2 root 7 × root 8 ×5 root 3 whole divided by 3 root 3 × root 15 ×root 42

To find: Simplify the above.

Solution:

Now we have given:

{ 2√7 x √8 x 5√3 } / { 3√3 x √15 x √42 }

Now we can write it as:

{ 2√7 x √2 x √2 x √2 x √5 x √5 x√3 } / { 3√3 x √3 x √5 x √7 x √3 x √2 }

Cancelling the similar terms from numerator and denominator such as √2, √3, √5 and √7, we get:

{ 2 x √2 x √2 x √5 }/ { 3√3 x √3 }

{2 x √5 } / 9

So the final simplification is:

2√5/9 = 0.4969

Answer 2

Answer:

$\frac{2 \sqrt{8} }{2 \sqrt{5} - \sqrt{3} } \\ = \frac{4 \sqrt{2} }{2 \sqrt{5} - \sqrt{3} } \times \frac{2 \sqrt{5} + \sqrt{3} }{2 \sqrt{5} + \sqrt{3} } \\ = \frac{4 \sqrt{2} (2 \sqrt{5} + \sqrt{3} )}{ {(2 \sqrt{5} )}^{2} - {( \sqrt{3} )}^{2} } \\ = \frac{8 \sqrt{10} + 4 \sqrt{6} }{20 - 3} \\ \frac{8 \sqrt{10} + 4 \sqrt{6} }{17}$