SIMPLIFYING SURDS

Write the following in simplest surd form :

Problem 1 :

√24

Solution :

√24

This can be written as,

= √(6 × 4)

= √6 × √4

= 2√6

So, the answer is 2√6.

Problem 2 :

√50

Solution :

√50

This can be written as,

= √(25 × 2)

= √25 × √2

= 5√2

So, the answer is 5√2.

Problem 3 :

√54

Solution :

√54

This can be written as,

= √(6 × 9)

= √6 × √9

= 3√6

So, the answer is 3√6.

Problem 4 :

√40

Solution :

√40

This can be written as,

= √(10 × 4)

= √10 × √4

= 2√10

So, the answer is 2√10.

Problem 5 :

√56

Solution :

√56

This can be written as,

= √(14 × 4)

= √14 × √4

= 2√14

So, the answer is 2√14.

Problem 6 :

√63

Solution :

√63

This can be written as,

= √(9 × 7)

= √9 × √7

= 3√7

So, the answer is 3√7.

Problem 7 :

√52

Solution :

√52

This can be written as,

= √(13 × 4)

= √13 × √4

= 2√13

So, the answer is 2√13.

Problem 8 :

√44

Solution :

√44

This can be written as,

= √(11 × 4)

= √11 × √4

= 2√11

So, the answer is 2√11.

Problem 9 :

√60

Solution :

√60

This can be written as,

= √(15 × 4)

= √15 × √4

= 2√15

So, the answer is 2√15.

Problem 10 :

√90

Solution :

√90

This can be written as,

= √(10 × 9)

= √10 × √9

= 3√10

So, the answer is 3√10.

Problem 11 :

√96

Solution :

√96

This can be written as,

= √(16 × 6)

= √16 × √6

= 4√6

So, the answer is 4√6.

Problem 12 :

√68

Solution :

√68

This can be written as,

= √(17 × 4)

= √17 × √4

= 2√17

So, the answer is 2√17.

Problem 13 :

√175

Solution :

√175

This can be written as,

= √(25 × 7)

= √25 × √7

= 5√7

So, the answer is 5√7.

Problem 14 :

√162

Solution :

√162

This can be written as,

= √(81 × 2)

= √81 × √2

= 9√2

So, the answer is 9√2.

Problem 15 :

√128

Solution :

√128

This can be written as,

= √(64 × 2)

= √64 × √2

= 8√2

So, the answer is 8√2.

Problem 16 :

√700

Solution :

√700

This can be written as,

= √(25 × 28)

= √25 × √28

= 5√28

So, the answer is 5√28.