Compare the following pair of surds. i. 7 2 , 5 3

Here we have, 7 2 , 5 3 For comparing we take square of each number 7 2 2 = 7 × 7 × 2 × 2 = 49 × 2 = 98 and, 5 3 2 = 5 × 5 × 3 × 3 = 25 × 3 = 75 Clearly, 98 > 75 ∴ 7 2 > 5 3

Compare the following pair of surds. i. 7 2 , 5 3

Here we have, 7 2 , 5 3 For comparing we take square of each number 7 2 2 = 7 × 7 × 2 × 2 = 49 × 2 = 98 and, 5 3 2 = 5 × 5 × 3 × 3 = 25 × 3 = 75 Clearly, 98 > 75 ∴ 7 2 > 5 3

Compare the following pair of surds. 247 , 274

Here we have, 247 , 274 We take square of each number to compare, 247 2 = 247 And 274 2 = 274 Clearly, 247 < 274 Therefore, 247 < 274

Compare the following pair of surds. 2 7 , 28

Here we have, 2 7 , 28 We take square of each number to compare it accordingly, 2 7 2 = 2 × 2 × 7 × 7 = 4 × 7 = 28 And 28 2 = 28 Clearly, 28 = 28 ∴ 2 7 = 28

Compare the following pair of surds. 5 5 , 7 2

Given: 5 5 , 7 2 To compare we simply square the numbers given, 5 5 2 = 5 × 5 × 5 × 5 = 25 × 5 = 125 And 7 2 2 = 7 × 7 × 2 × 2 = 49 × 2 = 98 Clearly, 125 > 98 ∴ 5 5 > 7 2

Compare the following pair of surds. 4 42 , 9 2

Here we have, 4 42 , 9 2 4 42 2 = 4 × 4 × 42 × 42 = 16 × 42 = 672 And 9 2 2 = 9 × 9 × 2 × 2 = 81 × 2 = 162 Clearly, 672 > 162 ∴ 4 42 > 9 2

Compare the following pair of surds. 5 3 , 9

Here we have 5 3 , 9 ( 5 3 ) = 5 × 5 × 3 = 75 And 9 = 9 × 9 = 81 Clearly, 75 < 81 ∴ 5 3 < 9

Compare the following pair of surds. 7 , 2 5

Here we have 7 , 2 5 To compare two or more non-equiradical surds, first we have to convert them into equiradical surds. 7 = 7 × 7 = 49 and, 2 5 = 2 × 2 × 5 = 4 × 5 = 20 Clearly, 49 > 20 ∴ 7 > 2 5

Here we have, 5 3 + 8 3 As 3 is common in both, so we take it as common and then add accordingly. 5 3 + 8 3 = ( 5 + 8 ) 3 = 13 3 Hence, 5 3 + 8 3 = 13 3

Simplify. 9 5 – 4 5 + 125

Here we have 9 5 – 4 5 + 125 9 5 – 4 5 + 125 = 9 5 – 4 5 + 5 × 5 × 5 = 9 5 – 4 5 + 5 5 We take 5 as common from all, we get = ( 9 – 4 + 5 ) 5 = 10 5 Hence, 9 5 – 4 5 + 125 = 10 5