Math, asked by amru2, 1 year ago

rationalise the denominator of
$7 \div 3 \sqrt3 - 2 \sqrt{3} ]{?}$

Answers

Answered by sravan29

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

amru2: I did not understand

amru2: what

sravan29: Ur welcome mark me please

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