Question

simplify by rationalizing the denominator of 6 minus 4 root 3 upon 6 + 4 root 3

Answer 1

Answer:

Step-by-step explanation

Hope it helps

Answer 2

Answer:

The simplified form is

$\frac{6-4\sqrt3}{6+4\sqrt3}=-7+4\sqrt3$

Step-by-step explanation:

Given the expression

$\frac{6-4\sqrt3}{6+4\sqrt3}$

we have to simplify by rationalizing the denominator.

$\frac{6-4\sqrt3}{6+4\sqrt3}$

$\text{multiply and divide by }6-4\sqrt3$

$=\frac{6-4\sqrt3}{6+4\sqrt3}\times \frac{6-4\sqrt3}{6-4\sqrt3}$

$=\frac{(6-4\sqrt3)^2}{(6+4\sqrt3)(6-4\sqrt3)}$

By identity,

$(a-b)^2=a^2+b^2-2ab$

$(a-b)(a+b)=a^2-b^2$

$=\frac{36+48-48\sqrt3}{36-48}$

$=\frac{84-48\sqrt3}{-12}$

$=-7+4\sqrt3$

which is required simplified form