Question

If a3 =81 b3=72 then find ab=?

Answer 1

Given :

a³ = 81

b³ = 72

To Find : ab

Solution :

a³ = 81

b³ = 72

$\sqrt[3]{81} \times \sqrt[3]{72} \\ \sqrt[3]{81 \times 72} \\ \sqrt[3]{3 \times 3 \times 3 \times 3 \times 2 \times 2 \times 2 \times 3 \times 3} \\ \sqrt[3]{ {3}^{3} \times {3}^{3} \times {2}^{3} } \\ 3 \times 3 \times 2 \\ 18$
The required Value of ab = 18 .

#Be Brainly !!

Answer 2

Given ,

a³ = 81

a³ = 3 × 3 × 3 ×3

$a=\sqrt[3]{3\times3\times3\times3}\\\;\\a=\sqrt[3]{3^{3}\times3}\\\;\\a=3\times\sqrt[3]{3}\\\;\\a=3\times3^{\frac{1}{3}}\\\;\\Similarly,\\\;\\b^{3}=72\\\;\\b^{3}=3\times3\times2\times2\times2\\\;\\b=\sqrt[3]{3\times3\times2\times2\times2}\\\;\\b=\sqrt[3]{2^{3}\times3^{2}}\\\;\\b=2\times3^{\frac{2}{3}}$

Now,

$ab=(3\times3^{\frac{1}{3}})\times(2\times3^{\frac{2}{3}}\\\;\\ab=(3\times2)\times(3^{\frac{1}{3}}\times3^{\frac{2}{3}})\\\;\\ab=(6)\times(3^{\frac{1}{3}+\frac{2}{3}})\\\;\\ab=6\times3^{\frac{2+1}{3}}\\\;\\ab=6\times3^{\frac{3}{3}}\\\;\\ab=6\times3\\\;\\ab=18$

ab = 18