Calculate the square root of six times the square root of 49 divided by the cube root of eight plus two squared.
For this problem, we’ll need to make sure we remember our order of operations. We use PEMDAS to remind us of the order of operations. Following this order, parentheses, exponents, multiplication, and division from left to right, addition and subtraction from left to right. We’re gonna treat everything that’s under the radical like it’s in parentheses. And in our final step, we’ll take the square root of everything that was in the radical.
Inside the radical, do we have any exponents? We have both radicals and exponents. Two squared equals four. The square root of 49 equals seven. What is the cube root of eight. It’s something times itself three times that equals eight. And that’s two. Two times two times two equals eight. Bring down the remaining parts of the problem.
Now, we’ll need to multiply and divide, beginning on the left and moving to the right. Six times seven equals 42. And then, we’ll bring everything down. 42 divided by two equals 21. We finished our multiplication and division. We can move on to addition and subtraction. 21 plus four equals 25. And we’re ready to put that 25 back under the radical. We’ve simplified this problem so that it says the square root of 25. And we know that the square root of 25 is five.
The final answer is five.