Question

Please find the value of this one expression

Answer 1

Solving the expression
`\frac{2}{\sqrt[6]{8} }.√(2)-(-(18)/(√(81) ) -2)` we get 6

The answer is 6.

Explanation:

We need to find value of expression:
`\frac{2}{\sqrt[6]{8} }.√(2)-(-(18)/(√(81) ) -2)`

We know that
`√(81)=9`

Our expression will become

`\frac{2}{\sqrt[6]{8} }.√(2)-(-(18)/(√(81) ) -2)\\=\frac{2}{\sqrt[6]{8} }.√(2)-(-(18)/(9 ) -2)\\=\frac{2}{\sqrt[6]{8} }.√(2)-(-2 -2)\\=\frac{2}{\sqrt[6]{8} }.√(2)-(-4)\\=\frac{2}{\sqrt[6]{8} }.√(2)+4`

We can write
`\sqrt[6]{8}=(2^3)^{(1)/(6)}=(2)^{(3)/(6)}=2^(1)/(2)=√(2) \\`

Now, replacing
`\sqrt[6]{8}=√(2)`

`=\frac{2}{\sqrt[6]{8} }.√(2)+4\\=(2)/(√(2) ).√(2)+4\\=2+4\\=6`

So, solving the expression
`\frac{2}{\sqrt[6]{8} }.√(2)-(-(18)/(√(81) ) -2)` we get 6