Question

Simplify by rationalising the denominator
​

Answer 1

Answer:

$\frac{9.04}{30}$

Step-by-step explanation:

$\frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} } \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{ 3} - 3 \sqrt{2} } \\ = \frac{21 \times 3 - 21 \sqrt{6} - 20 \sqrt{6} + 15 \times 2 }{16 \times 3 - 9 \times 2} \\ = \frac{61 + 30 - 21 \sqrt{6} - 20 \sqrt{6} }{48 - 18} \\ = \frac{91 - 41 \sqrt{6} }{30} \\ = \frac{91 - 41 \times 2.44}{30} \\ = \frac{91 - 100.04}{30} \\ = \frac{9.04}{30} \\ =$

I HOPE IT HELP YOU

Answer 2

Answer:

9.04

Step-by-step explanation:

\begin{lgathered}\frac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} } \\ = \frac{7 \sqrt{3} - 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} } \times \frac{4 \sqrt{3} - 3 \sqrt{2} }{4 \sqrt{ 3} - 3 \sqrt{2} } \\ = \frac{21 \times 3 - 21 \sqrt{6} - 20 \sqrt{6} + 15 \times 2 }{16 \times 3 - 9 \times 2} \\ = \frac{61 + 30 - 21 \sqrt{6} - 20 \sqrt{6} }{48 - 18} \\ = \frac{91 - 41 \sqrt{6} }{30} \\ = \frac{91 - 41 \times 2.44}{30} \\ = \frac{91 - 100.04}{30} \\ = \frac{9.04}{30} \\ =\end{lgathered}

48

+

18

7

3

−5

2

=

4

3

+3

2

7

3

−5

2

×

4

3

−3

2

4

3

−3

2

=

16×3−9×2

21×3−21

6

−20

6

+15×2

=

48−18

61+30−21

6

−20

6

=

30

91−41

6

=

30

91−41×2.44

=

30

91−100.04

=

30

9.04

=

I HOPE IT HELP YOU