Question : What is the third proportion of $2 \sqrt{3}$ and $6 \sqrt{5}$?
Option 1: $50 \sqrt{6}$
Option 2: $40 \sqrt{3}$
Option 3: $20 \sqrt{6}$
Option 4: $30 \sqrt{3}$
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Correct Answer: $30 \sqrt{3}$
Solution : Let the third proportion be $x$. $2 \sqrt{3}:6 \sqrt{5}::6 \sqrt{5}:x$ ⇒ $\frac{2 \sqrt{3}}{6 \sqrt{5}}=\frac{6 \sqrt{5}}{x}$ ⇒ $x=\frac{180}{2 \sqrt{3}}$ $\therefore x=30 \sqrt{3}$ Hence, the correct answer is $30 \sqrt{3}$.
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Question : What is the fourth proportional of $3 \sqrt{5}, 5 \sqrt{8}$, and $3 \sqrt{10}$?
Question : Which of the following is true?
Question : The ratio of three numbers is 6 : 5 : 9. If 20% of the first number is 30, then what would be 50% of the difference between the third and second numbers?
Question : If $x=(\sqrt{6}-1)^{\frac{1}{3}}$, then the value of $\left(x-\frac{1}{x}\right)^3+3\left(x-\frac{1}{x}\right)$ is:
Question : If $x=\frac{4\sqrt{15}}{\sqrt{5}+\sqrt{3}}$, the value of $\frac{x+\sqrt{20}}{x–\sqrt{20}}+\frac{x+\sqrt{12}}{x–\sqrt{12}}$ is:
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