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in Number System by (33.1k points)
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State which of the following are surds Justify.

i. \(\sqrt[3]{51}\)

ii. \(\sqrt[4]{16}\)

iii. \(\sqrt[5]{81}\)

iv. \(\sqrt{256}\)

v.\(\sqrt[3]{64}\)

vi.\(\sqrt{\frac{22}{7}}\)

1 Answer

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i.\(\sqrt[3]{51}\) is a surd because 51 is a positive rational number, 3 is a positive integer greater than 1 and \(\sqrt[3]{51}\) is irrational.

ii. \(\sqrt[4]{16}\) is not a surd because

= 2, which is not an irrational number.

iii. \(\sqrt[5]{81}\) s a surd because 81 is a positive rational number, 5 is a positive integer greater than 1 and \(\sqrt[5]{81}\) is irrational.

iv\(\sqrt{256}\) is not a surd because

= 16, which is not an irrational number.

v\(\sqrt[3]{64}\) is not a surd because

= 4, which is not an irrational number.

vi. \(\sqrt{\frac{22}{7}}\)is a surd because is a positive rational number, 2 is a positive integer greater than 1 and \(\sqrt{\frac{22}{7}}\)is irrational

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