Question

Can you answer pls? Give proper steps. The correct answer will be marked as brainliest.

Answer 1

Answer:

$\frac{4\sqrt{20} + 6\sqrt{30} + 10 \sqrt{40} }{2\sqrt{10} }$

= $\frac{2(2\sqrt{20}+ 3\sqrt{30} + 5 \sqrt{40} )}{2\sqrt{10} }$

= $\frac{2\sqrt{20}+ 3\sqrt{30} + 5 \sqrt{40} }{\sqrt{10} }$

= $\frac{4\sqrt{5} + 3\sqrt{30} + 10\sqrt{10} }{\sqrt{10} }$

Rationalizing factor = √10

$\frac{4\sqrt{5} + 3\sqrt{30} + 10\sqrt{10} }{\sqrt{10} }$  X  $\frac{\sqrt{10} }{\sqrt{10} }$

= $\frac{(4\sqrt{5} + 3\sqrt{30} + 10\sqrt{10} ) X \sqrt{10} }{\sqrt{10} X \sqrt{10} }$

= $\frac{4\sqrt{50}+ 3\sqrt{300}+ (10 X( \sqrt{10} X \sqrt{10})) }{10}$

= $\frac{4\sqrt{50}+ 3\sqrt{300}+ 10 X 10 }{10}$

= $\frac{4\sqrt{50}+ 3\sqrt{300}+100 }{10}$

= $\frac{20 \sqrt{2} + 30\sqrt{3}+100 }{10}$

= $\frac{10 (2\sqrt{2} + 3\sqrt{3}+ 10) }{10}$

$2\sqrt{2} + 3\sqrt{3} + 10$

∴ The answer is $2\sqrt{2} + 3\sqrt{3} + 10$  .