Question 1: State with reason which of the following are surds.

(i) . Therefore it is surd.

(ii) . This is a surd.

(iii) : We observe that is an irrational number. But, is not a rational number. Hence is not a surd.

(iv) . cannot be expresses as a rational number under a root sign. Therefore is not a surd.

(v) . Therefore it is a surd.

Question 2: Simplify the following:

(i)

(ii)

(iii)

(iv)

(v)

Question 3: Express the following as pure surds:

(i)

(ii)

(iii)

(iv)

(v)

Question 4: Express each of the following as a mixed surd in simplest form:

(i)

(ii)

(iii)

(iv)

(v)

Question 5: Convert:

(i) into a surd of order

(ii) into a surd of order

(iii) and into surds of the same but smallest order

LCM of and is

(iv) and into surds of the same but smallest order

LCM of and is

(v) into a surd of order

Question 6: Which is greater?

(i)

LCM of and is

(ii)

LCM of and is

(iii)

LCM of and is

(iv)

First simplify each of the given terms

For both the terms, the numerator is the same which is 4. Therefore whichever term has a higher denominator, would be the smaller term. Let’s compare the two denominators.

(v)

First simplify each of the given terms

For both the terms, the numerator is the same which is 5. Therefore whichever term has a higher denominator, would be the smaller term. Let’s compare the two denominators.

Question 7: Arrange in Ascending Order:

(i)

LCM of

Now convert all the above terms to order of 12

Now comparing the number under the root sign as they are all of the same order.

or

(ii)

LCM of

Now convert all the above terms to order of 12

Now comparing the number under the root sign as they are all of the same order.

or

Question 8: Arrange in Descending Order:

(i)

Convert into simple surds

Since the order of all the terms is the same, just compare the terms inside the square root. Hence, the descending order is

(ii)

LCM of

Now convert all the above terms to order of 24

Now comparing the number under the root sign as they are all of the same order.

or

Question 9: Simplify:

(i)

(ii)

(iii)

(iv)

(v)

Question 10: Multiply

(i)

(ii)

(iii)

LCM of

(iv)

(v)

Question 11: Divide

(i)

(ii)

(iii)

(iv)

(v)