The cube root of x varies inversely as the square root of y. x=8 when y=3. What is the value of x when y=\sqrt{3}?

Explanation

Given \sqrt{x} = \frac{k}{\sqrt{y}}. Substituting x=8, y=3 gives 2 = \frac{k}{\sqrt{3}} \implies k=2\sqrt{3}. When y=3^{1/3}, \sqrt{x} = \frac{2\sqrt{3}}{(3^{1/3})^{1/2}} = \frac{2 \times 3^{1/2}}{3^{1/6}} = 2 \times 3^{1/3}. Cubing both sides yields x = 8 \times 3 = 24.

Related questions on Arithmetic

• What is the remainder when (17^{25} + 19^{25}) is divided by 18?
• A bottle contains spirit and water in the ratio 1:4 and another identical bottle contains spirit and water in the ratio 4:1. In what rat...
• Let P = 5^5 \times 15^{15} \times 25^{25} \times 35^{35} and Q = 10^{10} \times 20^{20} \times 30^{30} \times 40^{40}. What is the numbe...
• Two students X and Y appeared in a test. The score of X is 20 more than that of Y. If the score of X is 75% of the sum of the scores of X an...
• Question: The product of a natural number N and the number M written by the same digits of N in the reverse order is 252. What is the number...