Question

Q.simplifyyyyyyyyyyyy

Answer 1

6/3rt2 - 2rt3 = 6/[rt3 * rt3 * rt2 - rt2 * rt2 *rt3]
= 6/rt3*rt2(rt3 - rt2)
= rt6*rt6/rt6(rt3 - rt2) = rt6/(rt3 - rt2)
Now, rationalising the denominator:
rt6*(rt3+rt2)/(rt3-rt2)*(rt3+rt2)
= rt2*rt3(rt3 + rt2)/3-2
= 3rt2 + 2rt3
Hence, answer = 3*root2 + 2*root3.
Hope it helps.
[you can also rationalize the denominator using: 3rt2 + 2rt3 in the first step instead of the simplification process that i'd done]

Answer 2

Answer:

$3\sqrt{2} +2\sqrt{3}$

Step-by-step explanation:

6/3rt2 - 2rt3 = 6/[rt3 * rt3 * rt2 - rt2 * rt2 *rt3]

= 6/rt3*rt2(rt3 - rt2)

= rt6*rt6/rt6(rt3 - rt2) = rt6/(rt3 - rt2)

Now, rationalising the denominator:

rt6*(rt3+rt2)/(rt3-rt2)*(rt3+rt2)

= rt2*rt3(rt3 + rt2)/3-2

= 3rt2 + 2rt3

Hence, answer = 3*root2 + 2*root3.

Hope it helps.

[you can also rationalize the denominator using: 3rt2 + 2rt3 in the first step instead of the simplification process that i'd done]