Question

simplify root 216 - 5 root 6 + root 294 - 3 upon root 6

Answer 1

Answer:

$\sqrt{216}-5\sqrt6+\sqrt{294}-\frac{3}{\sqrt6}=18.37$

Step-by-step explanation:

Given : Expression $\sqrt{216}-5\sqrt6+\sqrt{294}-\frac{3}{\sqrt6}$

To find : Simplify the expression ?

Solution :

$\sqrt{216}-5\sqrt6+\sqrt{294}-\frac{3}{\sqrt6}$

We can write,

$216=2\times 2\times 2\times 3\times 3\times 3\\\\\sqrt{216}=6\sqrt{6}$

$294=2\times 3\times 7\times 7\\\\\sqrt{294}=7\sqrt{6}$

Substitute,

$=6\sqrt{6}-5\sqrt6+7\sqrt{6}-\frac{3}{\sqrt6}$

Taking LCM,

$=\frac{6\times 6-5\times 6+7\times 6-3}{\sqrt6}$

$=\frac{36-30+42-3}{\sqrt6}$

$=\frac{45}{\sqrt6}$

$=\frac{45}{2.449}$

$=18.37$

Therefore, $\sqrt{216}-5\sqrt6+\sqrt{294}-\frac{3}{\sqrt6}=18.37$

Answer 2

$\frac{45}{\sqrt{6} }$

Step-by-step explanation:

Given,

$\sqrt{216}$ - 5 $\sqrt{6}$ + 6 $\sqrt{7}$ - $\frac{3}{\sqrt{6} }$

6 $\sqrt{6}$ - 5 $\sqrt{6}$ + 6 $\sqrt{7}$ - $\frac{3}{\sqrt{6} }$

$\frac{(6 \sqrt{6}* \sqrt{6}) - (5\sqrt{6}*\sqrt{6}) + (7\sqrt{6}*\sqrt{6}) - 3 }{\sqrt{6} }$

$\frac{(6*6) - (5* 6) + (7 * 6) - 3}{\sqrt{6} }$

$\frac{36 - 30 + 42 - 3}{\sqrt{6} }$

$\frac{78- 33}{\sqrt{6} }$

$\frac{45}{\sqrt{6} }$

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