compare Start Root 27 End Root and Start Fraction 22 over 3 End Fraction using either <, >, or =.
Start Root 27 End Root = 3, because the square root of 27 is 3.
Start Fraction 22 over 3 End Fraction = 7.333, because 22 divided by 3 is approximately 7.333.
Since 3 is not equal to 7.333, we can conclude that Start Root 27 End Root is not equal to Start Fraction 22 over 3 End Fraction. Therefore, we can use the inequality symbol ">" to compare them:
Start Root 27 End Root > Start Fraction 22 over 3 End Fraction
To compare the expressions "Start Root 27 End Root" and "Start Fraction 22 over 3 End Fraction", we need to evaluate each expression and compare the results.
1. Start Root 27 End Root:
To simplify this expression, we need to find the square root of 27, which is approximately 5.196.
2. Start Fraction 22 over 3 End Fraction:
To simplify this expression, we need to divide 22 by 3, which is approximately 7.333.
Now we can make the comparison:
5.196 < 7.333
Therefore, "Start Fraction 22 over 3 End Fraction" is greater than "Start Root 27 End Root".
To compare the expressions "Start Root 27 End Root" and "Start Fraction 22 over 3 End Fraction," we need to simplify both expressions.
First, let's simplify "Start Root 27 End Root":
The square root of 27 can be written as √27. We can simplify this further by finding the square root of 27:
√27 = √(9 * 3) = √9 * √3 = 3 * √3 = 3√3
Now let's simplify "Start Fraction 22 over 3 End Fraction":
The expression "22/3" is already in fraction form, so we don't need to simplify it further.
So we have:
Start Root 27 End Root = 3√3
Start Fraction 22 over 3 End Fraction = 22/3
To compare these two expressions using either <, >, or =, we need to convert them to the same format. In this case, both expressions are already in different formats (a square root and a fraction), so we can't directly compare them.
However, we can approximate their values to compare them.
To approximate the value of 3√3, we can use a calculator:
3√3 ≈ 5.196
To approximate the value of 22/3, we divide 22 by 3:
22/3 = 7.3333 (rounded to four decimal places)
Now we can compare the approximations:
5.196 < 7.3333
Therefore, we can conclude that "Start Root 27 End Root" is less than "Start Fraction 22 over 3 End Fraction" (3√3 < 22/3).