rationalise the denominator of
![7 \div 3 \sqrt3 - 2 \sqrt{3} ]{?}](https://tex.z-dn.net/?f=+7+%5Cdiv+3+%5Csqrt3+-+2+%5Csqrt%7B3%7D+%5D%7B%3F%7D+ "7 \div 3 \sqrt3 - 2 \sqrt{3} ]{?}")
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1
Rationalize the denominator:
3
2
6
−
3
(
6
+
3
6
+
3
)
√
6
−√
3
3√
2
(
√
6
+√
3
√
6
+√
3
)
6
3
+
3
6
6
2
−
3
2
−
3
3
−
6
√
6
2
−√
3
2
6√
3
+3√
6
−
3−√
6
3
2 Factor out the common term
3
3
3
(
2
3
+
6
)
6
2
−
3
2
−
3
3
−
6
√
6
2
−√
3
2
3(2√
3
+√
6
)
−
3−√
6
3
3 Use this rule:
x
2
=
x
√
x
2
=x
3
(
2
3
+
6
)
6
−
3
2
−
3
3
−
6
6−√
3
2
3(2√
3
+√
6
)
−
3−√
6
3
4 Use this rule:
x
2
=
x
√
x
2
=x
3
(
2
3
+
6
)
6
−
3
−
3
3
−
6
6−3
3(2√
3
+√
6
)
−
3−√
6
3
5 Simplify
6
−
3
6−3 to
3
3
3
(
2
3
+
6
)
3
−
3
3
−
6
3
3(2√
3
+√
6
)
−
3−√
6
3
6 Cancel
3
3
2
3
+
6
−
3
3
−
6
2√
3
+√
6
−
3−√
6
3
7 Rationalize the denominator:
3
3
−
6
(
3
+
6
3
+
6
)
3−√
6
3
(
3+√
6
3+√
6
)
2
3
+
6
−
9
+
3
6
3
2
−
6
2
2√
3
+√
6
−
3
2
−√
6
2
9+3√
6
8 Factor out the common term
3
3
2
3
+
6
−
3
(
3
+
6
)
3
2
−
6
2
2√
3
+√
6
−
3
2
−√
6
2
3(3+√
6
)
9 Simplify
3
2
3
2
to
9
9
2
3
+
6
−
3
(
3
+
6
)
9
−
6
2
2√
3
+√
6
−
9−√
6
2
3(3+√
6
)
10 Use this rule:
x
2
=
x
√
x
2
=x
2
3
+
6
−
3
(
3
+
6
)
9
−
6
2√
3
+√
6
−
9−6
3(3+√
6
)
11 Simplify
9
−
6
9−6 to
3
3
2
3
+
6
−
3
(
3
+
6
)
3
2√
3
+√
6
−
3
3(3+√
6
)
12 Cancel
3
3
2
3
+
6
−
(
3
+
6
)
2√
3
+√
6
−(3+√
6
)
13 Simplify brackets
2
3
+
6
−
3
−
6
2√
3
+√
6
−3−√
6
14 Collect like terms
2
3
+
(
6
−
6
)
−
3
2√
3
+(√
6
−√
6
)−3
15 Simplify
2
3
−
3
2√
3
−3
Done
3
2
6
−
3
(
6
+
3
6
+
3
)
√
6
−√
3
3√
2
(
√
6
+√
3
√
6
+√
3
)
6
3
+
3
6
6
2
−
3
2
−
3
3
−
6
√
6
2
−√
3
2
6√
3
+3√
6
−
3−√
6
3
2 Factor out the common term
3
3
3
(
2
3
+
6
)
6
2
−
3
2
−
3
3
−
6
√
6
2
−√
3
2
3(2√
3
+√
6
)
−
3−√
6
3
3 Use this rule:
x
2
=
x
√
x
2
=x
3
(
2
3
+
6
)
6
−
3
2
−
3
3
−
6
6−√
3
2
3(2√
3
+√
6
)
−
3−√
6
3
4 Use this rule:
x
2
=
x
√
x
2
=x
3
(
2
3
+
6
)
6
−
3
−
3
3
−
6
6−3
3(2√
3
+√
6
)
−
3−√
6
3
5 Simplify
6
−
3
6−3 to
3
3
3
(
2
3
+
6
)
3
−
3
3
−
6
3
3(2√
3
+√
6
)
−
3−√
6
3
6 Cancel
3
3
2
3
+
6
−
3
3
−
6
2√
3
+√
6
−
3−√
6
3
7 Rationalize the denominator:
3
3
−
6
(
3
+
6
3
+
6
)
3−√
6
3
(
3+√
6
3+√
6
)
2
3
+
6
−
9
+
3
6
3
2
−
6
2
2√
3
+√
6
−
3
2
−√
6
2
9+3√
6
8 Factor out the common term
3
3
2
3
+
6
−
3
(
3
+
6
)
3
2
−
6
2
2√
3
+√
6
−
3
2
−√
6
2
3(3+√
6
)
9 Simplify
3
2
3
2
to
9
9
2
3
+
6
−
3
(
3
+
6
)
9
−
6
2
2√
3
+√
6
−
9−√
6
2
3(3+√
6
)
10 Use this rule:
x
2
=
x
√
x
2
=x
2
3
+
6
−
3
(
3
+
6
)
9
−
6
2√
3
+√
6
−
9−6
3(3+√
6
)
11 Simplify
9
−
6
9−6 to
3
3
2
3
+
6
−
3
(
3
+
6
)
3
2√
3
+√
6
−
3
3(3+√
6
)
12 Cancel
3
3
2
3
+
6
−
(
3
+
6
)
2√
3
+√
6
−(3+√
6
)
13 Simplify brackets
2
3
+
6
−
3
−
6
2√
3
+√
6
−3−√
6
14 Collect like terms
2
3
+
(
6
−
6
)
−
3
2√
3
+(√
6
−√
6
)−3
15 Simplify
2
3
−
3
2√
3
−3
Done
amru2:
I did not understand
what
Ur welcome mark me please
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