Question

√24/8+√54/9 is a rational number or not​

Answer 1

Step-by-step explanation:

Hey there!

\frac{ \sqrt{24} }{8} + \frac{ \sqrt{54} }{9}

8

24

+

9

54

\frac{ 2\sqrt{6} }{8} + \frac{3 \sqrt{6} }{9}

8

2

6

+

9

3

6

\frac{ \sqrt{6} }{4} + \frac{ \sqrt{6} }{3}

4

6

+

3

6

\frac{ \sqrt{6} \times 3 }{4 \times 3} + \frac{ \sqrt{6} \times 4}{3 \times 4}

4×3

6

×3

+

3×4

6

×4

\frac{3 \sqrt{6} }{12} + \frac{4 \sqrt{6} }{12}

12

3

6

+

12

4

6

\frac{7 \sqrt{6} }{12}

12

7

6

Hope it helps!

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

$\sf{ \frac{ \sqrt{24} }{8} + \frac{ \sqrt{54} }{9} }$

$\sf{ = \frac{ \sqrt{4 \times 6} }{8} + \frac{ \sqrt{9 \times 6} }{9} }$

$\sf{ = \frac{2 \sqrt{6} }{8} + \frac{3 \sqrt{6} }{9} }$

$\sf{ = \frac{ \sqrt{6} }{4} + \frac{ \sqrt{6} }{3} }$

$\sf{ = \sqrt{6} \bigg( \frac{1}{4} + \frac{1}{3} \bigg) }$

$\sf{ = \sqrt{6} \bigg( \frac{3 + 4}{12} \bigg) }$

$\sf{ = \frac{7 \sqrt{6} }{12} \: \bf{Ans. }}$