Question

If \[\sqrt{2} = 1 . 414,\] then the value of \[\sqrt{6} - \sqrt{3}\] upto three places of decimal is

Options

•  0.235

• 0.707

• 1.414

• 0.471

Answer 1

Given that`sqrt2 = 1.414` .We need to find `sqrt6 - sqrt3`.

We can factor out from the given expression, to get

 `sqrt6 - sqrt3 = sqrt3(sqrt2 - 1)`.

Putting the value of`sqrt2`, we get

`sqrt3 (sqrt2-1) = sqrt3(1.4142 - 1)`

                      `=1.732xx0.4142`

                      `= 0.7174`

Hence the value of expression must closely resemble be`0.707.`