Question

State which of the following are surds. Justify (solve ) √2​

Answer 1

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Surds are numbers left in root form to express its exact value.

As,

351 cannot be expressed without root form. Hence, it is a surd.

Also,

416 =2, 481 =3, 256

=16. So, they are not surd.

i. 3 √ 51 513 is a surd because 51 is a positive rational number, 3 is a positive integer greater than 1 and 3 √ 51 513 is irrational.

ii. 4 √ 16 164 is not a surd because = 2, which is not an irrational number.

iii. 5 √ 81 815 is a surd because 81 is a positive rational number, 5 is a positive integer greater than 1 and 5 √ 81 815 is irrational.

iv. √ 256 256 is not a surd because = 16, which is not an irrational number.

v. 3 √ 64 643 is not a surd because = 4, which is not an irrational number.

vi. √ 22 / 7 22/7 is a surd because 22/7 is a positive rational number, 2 is a positive integer greater than 1 and √ 22 / 7 22/7 is irrational.

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