Evaluate square root expression
Published:
$$\sqrt{33^4 - 22^4 - 11^4} = ?$$
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Step by Step Written Solution
Hi Türkan, let's solve this interesting radical expression together by using some clever factoring.
Solving the Expression
Notice that thirty-three, twenty-two, and eleven are all multiples of eleven.
We can rewrite each term using eleven as a factor: thirty-three is three times eleven, and twenty-two is two times eleven.
Now, distribute the exponent of four to each part inside the parentheses.
Next, we factor out the common term, which is eleven to the power of four.
Now, let's calculate the values inside the parentheses. Three to the power of four is eighty-one, two to the power of four is sixteen, and one to the power of four is simply one.
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