Question

How do you evaluate `6+ \sqrt { 245}`?

Answer 1

See a solution process below:

Explanation:

First, we can rewrite this expression as:

`6 + sqrt(49 * 5)`

Using this rule of exponents we can simplify the term in the radical:

`sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))`

`6 + sqrt(color(red)(49) * color(blue)(5)) => 6 + (sqrt(color(red)(49)) * sqrt(color(blue)(5))) =>`

`6 + 7sqrt(5)`

If the requirement is to evaluate this to a single number then the `sqrt(5) = 2.236` rounded to the nearest thousandth. Substituting this into the previous expression gives:

`6 + (7 * 2.236) => 6 + 15.652 => 21.652`