Question

If √2=1.414 and √3=1.732 then find the value of √6-1/√3 up to three places of decimal

Answer 1

Answer:

$\sqrt{6} - \frac{1}{ \sqrt{3} } \\ = \sqrt{2 \times 3} - \frac{1}{ \sqrt{3} } \\ = \frac{3 \sqrt{2} - 1}{ \sqrt{3} } \\ = \frac{3(1.414) - 1}{1.732} \\ = \frac{4.242 - 1}{1.732} \\ = \frac{3.242}{1.732} \\ = 1.87$

Answer 2

Step-by-step explanation:

The value of \frac { \sqrt { 6 } - 1 } { \sqrt { 3 } }

3

6

−1

up to 3 places of decimal point will be 0.837.

To find:

The value of the given expression \frac { \sqrt { 6 } - 1 } { \sqrt { 3 } }

3

6

−1

up to three places of decimal point.

Solution:

Given that the value of \sqrt2

2

and \sqrt3

3

will be

\sqrt { 2 } = 1.414

2

=1.414

and

\sqrt { 3 } = 1.732

3

=1.732

Thus the value of

\begin{lgathered}\begin{array} { l } { \frac { \sqrt { 6 } - 1 } { \sqrt { 3 } } = \frac { \sqrt { 2 } \times \sqrt { 3 } - 1 } { \sqrt { 3 } } } \\\\ { = \frac { 1.414 \times 1.732 - 1 } { 1.732 } } \\\\ { = \frac { 2.449048 - 1 } { 1.732 } } \\\\ { = \frac { 1.443048 } { 1.732 } } \\\\ { = 0.8366 } \end{array}\end{lgathered}

3

6

−1

=

3

2

×

3

−1

=

1.732

1.414×1.732−1

=

1.732

2.449048−1

=

1.732

1.443048

=0.8366

\begin{lgathered}\begin{array} { c } { \frac { \sqrt { 6 } - 1 } { \sqrt { 3 } } = 0.8366 } \\\\ { \frac { \sqrt { 6 } - 1 } { \sqrt { 3 } } = 0.8366 \approx 0.837 } \end{array}\end{lgathered}

3

6

−1

=0.8366

3

6

−1

=0.8366≈0.837

Thus the value of \frac { \sqrt { 6 } - 1 } { \sqrt { 3 } }

3

6

−1

up to 3 places of decimal will be 0.837.