Question

2 root 30 by root 6 minus 2root 140 by28+root55 by root 99

Answer 1

Answer:

$2\sqrt{5}-\frac{\sqrt{35}}{7} +\frac{\sqrt{5}}{3}}$

Step-by-step explanation:

Given: $\frac{2\sqrt{30} }{\sqrt{6} }-\frac{2\sqrt{140} }{28} +\frac{\sqrt{55} }{\sqrt{99} }$

We have to write  the given expression in simplest form.

Consider the given expression,

$\frac{2\sqrt{30} }{\sqrt{6} }-\frac{2\sqrt{140} }{28} +\frac{\sqrt{55} }{\sqrt{99} }$

Simplify, we get,

$\frac{2\sqrt{30} }{\sqrt{2}\sqrt{3}}-\frac{2\sqrt{140} }{28} +\frac{\sqrt{55} }{\sqrt{99} }$

Solving further, we get,

$\frac{2(\sqrt{2}\sqrt{3}\sqrt{5})}{\sqrt{2}\sqrt{3}}-\frac{2\sqrt{140} }{28} +\frac{\sqrt{55} }{\sqrt{99} }$

Cancelling , we get

$2\sqrt{5}-\frac{2\sqrt{140} }{28} +\frac{\sqrt{55} }{\sqrt{99} }$

Simplify, we get,

$2\sqrt{5}-\frac{2(2\sqrt{5}\sqrt{7}) }{28} +\frac{\sqrt{55} }{\sqrt{99} }$

Solving, we get,

$2\sqrt{5}-\frac{\sqrt{35}}{7} +\frac{\sqrt{55} }{\sqrt{99} }$

$2\sqrt{5}-\frac{\sqrt{35}}{7} +\frac{\sqrt{5}\sqrt{11} }{3\sqrt{11} }$

Simplify, we get,

$2\sqrt{5}-\frac{\sqrt{35}}{7} +\frac{\sqrt{5}}{3}}$