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