√71 < √61
√81 > 9
√71 > √61
√81 < 9
False
True
True
False
To compare the given expressions involving square roots:
√71 < √61:
To determine which square root is larger, we need to compare their values. Since both numbers are not perfect squares, we can approximate their values using a calculator.
√71 is approximately 8.426, and √61 is approximately 7.810. Since 8.426 is greater than 7.810, we can conclude that √71 is greater than √61.
√81 > 9:
To compare these expressions, we need to simplify them. √81 is the square root of a perfect square, which is 9. Since 9 is equal to 9, we can say that √81 is equal to 9. Being equal, √81 is not greater than 9.
√71 > √61:
As we determined previously, √71 is approximately 8.426, and √61 is approximately 7.810. Since 8.426 is greater than 7.810, we can conclude that √71 is indeed greater than √61.
√81 < 9:
Since √81 is equal to 9, we can say that √81 is equal to 9. Being equal, √81 is not less than 9.