Question

if √2=1.414 and √3=1.732 then find the value of √6-1/ √3

Answer 1

Solution:

$\dfrac{ \sqrt{6} - 1}{ \sqrt{3} }$

To rationalize the denominator, multiply √3 in both numerator and denominator.

$\dfrac{ \sqrt{3} ( \sqrt{6} - 1)}{ \sqrt{3} \times \sqrt{3} }$

Now we have

$= \dfrac{ \sqrt{18} - \sqrt{3} }{3}$

√18 can be written as √9 × √2 which is nothing but √(9×2)

$\implies \dfrac{ \sqrt{9 \times 2} - \sqrt{3} }{3}$

Square root of 9 is 3. So,

$\implies \dfrac{3 \sqrt{2} - \sqrt{3} }{3}$

Substitute the given values in this expression.

$\implies \dfrac{3(1.414) - 1.732}{3}$

$\dashrightarrow \: \dfrac{4.242 - 1.732}{3}$

$=\dfrac{2.51}{3}$

$= \boxed{ \bf{0.8366}}$

∴ (√6 - 1)/√3 = 0.8366

KNOW MORE:

• Whenever a irrational number is given in the denominator, first rationalize it and then substitute the given values to get the required a answer