To find the value of the expression [tex]\(\frac{250}{30} \sqrt{\theta}\)[/tex], we will go through the following steps:
1. Simplify the fraction:
[tex]\[\frac{250}{30}\][/tex]
To simplify this fraction, we can divide both the numerator (250) and the denominator (30) by their greatest common divisor. The greatest common divisor of 250 and 30 is 10.
[tex]\[\frac{250 \div 10}{30 \div 10} = \frac{25}{3}\][/tex]
2. Express the simplified fraction as a decimal:
We need to convert [tex]\(\frac{25}{3}\)[/tex] to a decimal for easier multiplication with [tex]\(\sqrt{\theta}\)[/tex].
[tex]\[\frac{25}{3} \approx 8.333333333333334\][/tex]
3. Formulate the final expression:
Now, we multiply this simplified value by [tex]\(\sqrt{\theta}\)[/tex].
The final expression is:
[tex]\[ \frac{250}{30} \sqrt{\theta} \approx 8.33333333333333 \sqrt{\theta} \][/tex]
Therefore, the expression [tex]\(\frac{250}{30} \sqrt{\theta}\)[/tex] simplifies to approximately [tex]\(8.33333333333333 \sqrt{\theta}\)[/tex].
