ARRANGING SURDS IN DESCENDING ORDER

Question 1 :

Solution :

Exponential form of given radical terms.

5^1/3, 4^1/9, 3^1/6

L.C.M of 3, 9 and 6 is 18.

(ii)  Exponential form of given radical terms.

5^1/6, 7^1/12, 3^1/4

Solution :

Question 2 :

Can you get a pure surd when you find

(i) the sum of two surds

(ii) the difference of two surds

(iii) the product of two surds

(iv) the quotient of two surds

Justify each answer with an example.

Solution :

(i)  Let us take an example,

√2 + √2  =  2 √2

Convert into pure surd, we get

2√2  =  √8

√8 is pure surd. Hence the answer is yes.

(ii)  √10 - √5  =  √5

Convert into pure surd, we get

 √10 - √5  =  √5(√2 - 1)

Hence the answer is yes.

(iii) the product of two surds

 √10 x √5  =  √50

Hence the answer is yes.

(iv) the quotient of two surds

 √(35/7)  =  √5

Hence the answer is yes.

Can you get a rational number when you compute

(i) the sum of two surds

(ii) the difference of two surds

(iii) the product of two surds

(iv) the quotient of two surds

Justify each answer with an example.

Solution :

Every integer can be written as rational number. Hence the answer is yes.

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