Express the surd in simplest form. 96

A surd is said to be in its simplest form when the number under the root sign has no square factors. Given, 96 Prime factors of 96 is 2 × 2 × 2 × 2 × 2 × 3 So, 2 × 2 × 2 × 2 × 2 × 3 = 2 × 2 2 × 3 = 4 6 Thus, the simplest form of 96 is 4 6 .

Express the surd in simplest form. 96

A surd is said to be in its simplest form when the number under the root sign has no square factors. Given, 96 Prime factors of 96 is 2 × 2 × 2 × 2 × 2 × 3 So, 2 × 2 × 2 × 2 × 2 × 3 = 2 × 2 2 × 3 = 4 6 Thus, the simplest form of 96 is 4 6 .

Express the surd in simplest form. 112

A surd is said to be in its simplest form when the number under the root sign has no square factors. Given, 112 Prime factors of 112 is 2 × 2 × 2 × 2 × 2 × 7 So, 2 × 2 × 2 × 2 × 7 = 2 × 2 7 = 4 7 Thus, the simplest form of 112 is 4 7 .

Express the surd in simplest form. 162

A surd is said to be in its simplest form when the number under the root sign has no square factors. Given, 162 Prime factors of 162 is 2 × 3 × 3 × 3 × 3 So, 2 × 3 × 3 × 3 × 3 = 3 × 3 2 = 9 2 Thus, the simplest form of 162 is 9 2 .

Express the surd in simplest form. 245

A surd is said to be in its simplest form when the number under the root sign has no square factors. Given, 245 Prime factors of 245 is 5 × 7 × 7 So, 5 × 7 × 7 = 7 5 Thus, the simplest form of 245 is 7 5 .

Write the simplest rationalising factor of : 48

When a surd is multiplied by another surd to obtain a rational number, it is called rationalisation. Each surd is called the rationalising factor of the other. Given, 48 Prime factors of 48 is 2 × 2 × 3 × 2 × 2 So, 48 = 2 × 2 × 3 × 2 × 2 = 2 × 2 × 3 = 4 3 If we multiply 4 3 by 3 , we get 4 3 × 3 = 4 × 3 = 12 → rational number Hence, 3 is the rationalising factor of 4 3 .

Write the simplest rationalising factor of : 72

When a surd is multiplied by another surd to obtain a rational number, it is called rationalisation. Each surd is called the rationalising factor of the other. Given, 72 Prime factors of 72 is 2 × 2 × 2 × 3 × 3 So, 72 = 2 × 2 × 2 × 3 × 3 = 2 × 3 × 2 = 6 2 If we multiply 6 2 by 2 , we get 6 2 × 2 = 6 × 2 = 12 → rational number Hence, 2 is the rationalising factor of 6 2 .

Write the simplest rationalising factor of : 5 3 + 8

When a surd is multiplied by another surd to obtain a rational number, it is called rationalisation. Each surd is called the rationalising factor of the other. Given, 5 3 + 8 If we multiply 5 3 - 8 with 5 3 + 8 we will get 5 3 + 8 5 3 - 8 = 5 3 2 - 8 2 = 75 - 64 = 11 → rational number Hence, 5 3 - 8 is the rationalising factor of 5 3 + 8 .

Write the simplest rationalising factor of : 7 - 5

When a surd is multiplied by another surd to obtain a rational number, it is called rationalisation. Each surd is called the rationalising factor of the other. Given, 7 - 5 If we multiply 7 - 5 with 7 + 5 we will get 7 - 5 7 + 5 = 7 2 - 5 2 = 7 - 5 = 2 → rational number Hence, 7 + 5 is the rationalising factor of 7 - 5 .