What is the fourth proportional of 3√5, 5√8 and 3 √10?

Correct option is D

Given:

The given numbers are  $$3\sqrt{5}, 5\sqrt{8}, and 3\sqrt{10}.$$​​

Formula Used:

The fourth proportional x  can be found using the formula for fourth proportional:

​$$\frac{a}{b} = \frac{c}{x}$$​​

Solution:

​$$\frac{3\sqrt{5}}{5\sqrt{8}} = \frac{3\sqrt{10}}{x}\\x = \frac{3\sqrt{10} \times 5\sqrt{8}}{3\sqrt{5}}\\x = \frac{5 \times \sqrt{10} \times \sqrt{8}}{\sqrt{5}}\\\ \\x = \frac{5 \times \sqrt{80}}{\sqrt{5}}\\\ \\x = 5 \times \frac{\sqrt{80}}{\sqrt{5}}\\\ \\x = 5 \times \sqrt{16}\\\ \\x = 5 \times 4$$​​

Therefore, x = 20