Question

If√6=2.449,then value of 3√2/2√3 is close to:

Answer 1

Dear Student,

◆ Answer -

3√2/2√3 = 1.2245

● Explaination -

Let's take -

X = 3√2 / 2√3

X = (√3)²√2 / 2√3

X = √3 × √3 × √2 / 2√3

X = √(3×2) / 2

X = √6 / 2

Putting √6 = 2.449,

X = 2.449 / 2

X = 1.2245

Therefore, value of 3√2/2√3 = 1.2245.

Hope this was helpful...

Answer 2

Answer:

$if \: \: \sqrt{6} = 2.449$
$\frac{3 \sqrt{2} }{2 \sqrt{3} } =?$
As we have the value of √6,and we also know that ,whenever there was an irrational number in denominator we always do rationalization.

Now rationalize the denominator,by multiply √3 in both numerator and denominator

$\frac{3 \sqrt{2} \times \sqrt{3} }{2 \times \sqrt{3} \times \sqrt{3} } \\ \\ \\ = > \frac{3 \sqrt{2 \times 3} }{2 \times {( \sqrt{3} })^{2} } \\ \\ \\ = > \frac{3 \sqrt{6} }{2 \times 3} \\ \\ \\ = > \frac{ \sqrt{6} }{2} \\ \\ \\ = > \frac{2.449}{2} \\ \\ \\ \frac{3 \sqrt{2} }{2 \sqrt{3} } = > 1.2245$
Hope it helps you.

Note: √a × √b =√(a×b)