Question

How do you evaluate `sqrt(4\times 30+ 15)`?

Answer 1

See a solution process below:

Explanation:

First, we will treat the radical the same as a parenthesis and evaluate the terms within the radical first. Using the standard or of operation we will first execute the multiplication operation:

`sqrt(color(red)(4) xx color(red)(30) + 15) = sqrt(120 + 15)`

Next, execute the addition operation within the radical:

sqrt(color(red)(120) + color(red)(15)) = sqrt(135)#

We can rewrite this expression as:

`sqrt(9 * 15)`

Using this rule of radicals we can further evaluate the expression:

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

`sqrt(color(red)(9) * color(blue)(15)) = sqrt(color(red)(9)) * sqrt(color(blue)(15)) = 3 * sqrt(15) = 3sqrt(15)`

If necessary: `sqrt(15) = 3.873` rounded to the nearest thousandth.

Then:

`3sqrt(15) = 3 * 3.873 = 11.619` rounded to the nearest thousandth.