Convert 2.4 to radical form.

Converting a decimal number to its radical form involves expressing the number as a root of an integer. The decimal 2.4 is not a perfect square, so it cannot be expressed as a simple radical like √2 or √3. However, we can look for a rational number whose square is 2.4 and then express that number in radical form. We might reason that since 2.4 is close to 2.25, which is the square of 1.5, then the square root of 2.4 must be slightly larger than 1.5.
Although there is no nice rational square root of 2.4, for practical purposes, you can approximate it. One way to find an approximation is to use the property that (ab)^n = a^n b^n . We can write 2.4 as 24/10 to give us a fraction we can work with. We know that 24 is a perfect square since it is 2^2 × 3^2, and 10 is not a perfect square but can be written as 2 × 5. So, we can rewrite √2.4 in its radical form as √(24/10) which equals √(2² × 3²) / √(2 × 5).
However, for perfect squares like 4.0, it is straightforward to represent them in radical form. For example, √4.0 simply equals to 2. In your question, the expression (2x)^2 = 4.0 (1 - x)^2 can be simplified by taking the square root of both sides to get 2x = 2 · (1 - x), which simplifies further to 2x = 2 - 2x, and then x = 0.5 after rearranging.

Answered by qwarrow | 2024-06-18

To convert 2.4 to radical form, express it as 2.4 ​ , which simplifies to 10 ​ 2 6 ​ ​ . This involves converting it to a fraction and simplifying the square root. Thus, the radical form includes both a decimal approximation and a simplified radical expression.
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Answered by qwarrow | 2024-10-01