Question

rationalize the denominator 5/2√3-√2 ​

Answer 1

We have been asked to rationalise the denominator of :

$\large{ \sf{ \dfrac{5}{2 \sqrt{3} - \sqrt{2} }}}$

For that we need to follow up the given steps :

1. Check the sign in the denominator .
2. Take the opposite sign of the denominator with same numbers and multiply it with both the numerator and denominator
3. This creates an identity : (a+b)(a-b)
4. Simplify according to the identity .

Following the above steps ; the solution is this way :

S O L U T I O N :

$\longrightarrow{ \sf{ \dfrac{5}{2 \sqrt{3} - \sqrt{2} } }} \times \dfrac{2 \sqrt{3} + \sqrt{2} }{2 \sqrt{3} + \sqrt{2} }$

$\longrightarrow{ \sf{ \dfrac{5(2 \sqrt{3} + \sqrt{2}) }{ {2 \sqrt{3} }^{2} - { \sqrt{2} }^{2} } }}$

$\longrightarrow{ \sf{ \dfrac{5(2 \sqrt{3} + \sqrt{2}) }{(2 \times 2 \times 3) - 2} }}$

$\longrightarrow{ \sf{ \dfrac{5( 2 \sqrt{3} + \sqrt{2}) }{12 - 2} }}$

$\longrightarrow{ \sf{ \dfrac{5( 2 \sqrt{3} + \sqrt{2})}{ 10} }}$

So ; when denominator is rationalised :

$\longrightarrow{ \sf{ \dfrac{5( 2 \sqrt{3} + \sqrt{2})}{10} }}$

Answer 2

Questions

✩✩✩✩✩✩

$rationalize \: the \: denominator \: 5/2√3-√2$

✩ S O L U T I O N :✩

$\longrightarrow{ \sf{ \dfrac{5}{2 \sqrt{3} - \sqrt{2} } }} \times \dfrac{2 \sqrt{3} + \sqrt{2} }{2 \sqrt{3} + \sqrt{2} }$

$\longrightarrow{ \sf{ \dfrac{5(2 \sqrt{3} + \sqrt{2}) }{ {2 \sqrt{3} }^{2} - { \sqrt{2} }^{2} } }}$

$\longrightarrow{ \sf{ \dfrac{5(2 \sqrt{3} + \sqrt{2}) }{(2 \times 2 \times 3) - 2} }}$

$\longrightarrow{ \sf{ \dfrac{5( 2 \sqrt{3} + \sqrt{2}) }{12 - 2} }}$

$\longrightarrow{ \sf{ \dfrac{5( 2 \sqrt{3} + \sqrt{2})}{ 10} }}$

♡ So ; when denominator is rationalised :♡

$\longrightarrow{ \sf{ \dfrac{5( 2 \sqrt{3} + \sqrt{2})}{10} }}$