Express the surd in the simplest form: 8

Simplifying surds is where we rewrite a surd in its simplest form by ensuring the number underneath the root sign (this number is called the radicand) has no square numbers as factors. Given, 8 Write all prime factors of 8 under the root. 8 = 2 × 2 × 2 = 2 2 Thus, the simplest form is 2 2

Express the surds in the simplest form: 192 3

Simplifying surds is where we rewrite a surd in its simplest form by ensuring the number underneath the root sign (this number is called the radicand) has no square numbers as factors. Given, 192 3 So, prime factors of 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3 Now, 192 3 = 2 × 2 × 2 × 2 × 2 × 2 × 3 3 = 2 × 2 × 3 3 = 4 3 3 Thus, the simplified surd is 4 3 3

Show that 7 3 > 5 1 .

We have to show that 7 3 > 5 1 Convert the surds into same order surds to compare So, 7 3 = 7 4 12 = 2401 12 5 4 = 5 1 4 = 5 3 12 = 5 3 12 = 125 12 2401 12 > 125 12 Therefore, 7 3 > 5 4 .

Arrange in ascending order: 2 3 , 4 2 , 3 4

The order of the surds 2 3 , 4 2 and 3 4 are 3 , 2 , 4 . L.C.M. of 3 , 2 , 4 = 12 . 2 3 = 2 1 3 = 2 4 12 = 2 4 12 = 16 12 ; 4 2 = 4 1 2 = 4 6 12 = 4 6 12 = 4096 12 3 4 = 3 1 4 = 3 3 12 = 3 3 12 = 27 12 The ascending order of the surds 2 3 , 3 4 , 4 2 is 16 12 < 27 12 < 4096 12 that is, 2 3 , 3 4 , 4 2 .