Question

Root 6+root 3/root 6- root 3

Answer 1

The answer is 0.172

GIVEN

$\frac{ \sqrt{6 } + \sqrt{3} }{ \sqrt{6} - \sqrt{3} }$

TO FIND

To simplify the given expression.

SOLUTION

We can simply solve the above problem as follows;

We are given a mathematical expression,

$\frac{ \sqrt{6 } + \sqrt{3} }{ \sqrt{6} - \sqrt{3} }$

Multiplying √6 + √3 in denominator as well in numerator;

$= \frac{ \sqrt{6 } + \sqrt{3} }{ \sqrt{6} - \sqrt{3} } \times \frac{ \sqrt{6} + \sqrt{3} }{ \sqrt{6} + \sqrt{3} }$

Applying the formula, (a+b) (a-b) = a² - b², in the denominator.

$= \frac{ ( \sqrt{6} + \sqrt{3} ) ^{2} }{ ( \sqrt{6} )^{2} - ( \sqrt{3} )^{2} }$

Applying, (a+b)² = a² + b² + 2ab in the numerator;

$= \frac{ { \sqrt{6} }^{2} + { \sqrt{3} }^{2} + 2 \times \sqrt{3} \times \sqrt{3} }{6 - 3}$

$= \frac{6 - 2 \times \sqrt{6} \times \sqrt{3} + 3}{3}$

$= \frac{9 - 2 \sqrt{18} }{3}$

$= 3 - 2 \sqrt{2}$

= 3- 2 × 1.14

= 0.172

Hence, The answer is 0.172

#Spj2

Answer 2

Answer:

The answer to the given question is 5.828.

Step-by-step explanation:

Given :

$\frac{ \sqrt{6} + \sqrt{3} }{ \sqrt{6} - \sqrt{3} }$

To find :

We have to simplify the following expression.

Solution :

The given expression is

$\frac{ \sqrt{6} + \sqrt{3} }{ \sqrt{6} - \sqrt{3} }$

on rationalising the given expression is multiplied with the conjugate of the denominator

the conjugate term is

$\sqrt{6} - \sqrt{3} = \sqrt{6} + \sqrt{3}$

Multiply both the numerator and denominator with the conjugate term.

$\frac{ \sqrt{6} + \sqrt{3} }{ \sqrt{6} - \sqrt{3} } \times \frac{ \sqrt{6} + \sqrt{3} }{ \sqrt{6} + \sqrt{3} }$

On multiplying we get

$\frac{ {( \sqrt{6} + \sqrt{3}) }^{2} }{ {( \sqrt{6}) }^{2} - {(\sqrt{3}) }^{2} }$

on expanding we get,

The numerator should be expanded using the formula

${(x +y )}^{2} = {x}^{2} + {y}^{2} + 2xy$

Then on applying

$\frac{( { \sqrt{6} )}^{2} + {( \sqrt{3}) }^{2} + 2( \sqrt{6} )( \sqrt{3} ) }{6 - 3}$

on solving the square and square roots we get the values as

$\frac{(6 + 3 )+ 2 \times \sqrt{2} \times \sqrt{3} \times \sqrt{3} }{6 - 3}$

on further proceeding, we get the answer as

$\frac{9 + 2 \times 3 \times \sqrt{2} }{3} \\ \frac{9 + 6 \sqrt{2} }{3}$

The value of

$\sqrt{2 } = 1.414$

on substituting, we get

$\frac{9 + 6(1.414)}{3} = \frac{9 + 8.484}{3} \\ \frac{17.484}{3} \\ = 5.828$

on substituting, we got the final answer as

5.828.

This is the final value obtained.

# spj5

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