Simplify the following: 3 8 + 1 2

From the given, 3 8 + 1 2 First we convert the denominators into rational numbers. In the first term, multiply the numerator and denominator by 8 . 3 8 × 8 8 = 3 8 8 In the second term, multiply the numerator and denominator by 2 . 1 2 × 2 2 = 2 2 Now, we add 3 8 8 + 2 2 3 8 8 + 2 2 = 3 8 8 + 2 2 × 4 4 = 3 8 + 4 2 8 = 3 4 × 2 + 4 2 8 = 6 2 + 4 2 8 = 10 2 8 = 5 2 4 Therefore, 3 8 + 1 2 = 5 2 4

Simplify the following: 3 8 + 1 2

From the given, 3 8 + 1 2 First we convert the denominators into rational numbers. In the first term, multiply the numerator and denominator by 8 . 3 8 × 8 8 = 3 8 8 In the second term, multiply the numerator and denominator by 2 . 1 2 × 2 2 = 2 2 Now, we add 3 8 8 + 2 2 3 8 8 + 2 2 = 3 8 8 + 2 2 × 4 4 = 3 8 + 4 2 8 = 3 4 × 2 + 4 2 8 = 6 2 + 4 2 8 = 10 2 8 = 5 2 4 Therefore, 3 8 + 1 2 = 5 2 4

Simplify the following. 5 + 7 2 + 5

From the given, 5 + 7 2 + 5 We have to multiply the two irrational numbers by using normal multiplication method. We multiply each number of the first expression with each number of the second expression. 5 + 7 2 + 5 = 5 × 2 + 5 + 7 × 2 + 5 = 10 + 5 5 + 2 7 + 35 Hence, 5 + 7 2 + 5 = 10 + 5 5 + 2 7 + 35

Simplify the following. 5 - 2 2

From the given, 5 - 2 2 Use the identify: a - b 2 = a - 2 a b + b Here, a = 5 , b = 2 5 - 2 2 = 5 - 2 5 × 2 + 2 = 5 - 2 10 + 2 = 7 - 2 10 Hence, 5 - 2 2 = 7 - 2 10

Simplify the following. 3 + 7 2

From the given, 3 + 7 2 We know that, a + b 2 = a + 2 a b + b Here, a = 3 , b = 7 3 + 7 2 = 3 + 2 × 3 × 7 + 7 = 3 + 2 21 + 7 = 10 + 2 21 Hence, 3 + 7 2 = 10 + 2 21

Simplify the following. 2 + 3 5 + 7

From the given, 2 + 3 5 + 7 We have to multiply the two irrational numbers by using normal multiplication method. To multiply each number in the first bracket with each number in the second bracket. 2 + 3 5 + 7 = 2 × 5 + 7 + 3 × 5 + 7 = 2 × 5 + 2 × 7 + 3 × 5 + 3 × 7 = 10 + 14 + 15 + 21 So, 2 + 3 5 + 7 = 10 + 14 + 15 + 21 Hence, the required answer is as shown above.

Simplify the following. 4 + 5 3 - 7

From the given, 4 + 5 3 - 7 We have to multiply the two irrational numbers by using normal multiplication method. To multiply each number in the first bracket with each number in the second bracket. 4 + 5 3 - 7 = 4 × 3 - 7 + 5 × 3 - 7 = 4 3 - 4 7 + 5 × 3 - 5 × 7 = 4 3 - 4 7 + 15 - 35 So, 4 + 5 3 - 7 = 4 3 - 4 7 + 15 - 35 Hence, the required answer is as shown above.

Simplify the following. 50 - 98 + 162

From the given, 50 - 98 + 162 We have to simplify the given irrational numbers. First term, 50 = 25 × 2 = 5 2 Second term, 98 = 2 × 49 = 2 × 49 = 7 2 Third term, 162 = 2 × 81 = 2 × 81 = 9 2 Now, 50 - 98 + 162 = 5 2 - 7 2 + 9 2 = 14 2 - 7 2 = 7 2 Hence, 50 - 98 + 162 = 7 2

Simplify the following. 2 50 × 3 32 × 4 18

From the given, 2 50 × 3 32 × 4 18 We have to simplify the given irrational numbers. First term, 2 50 = 2 25 × 2 = 2 × 5 × 2 = 10 2 Second term, 3 32 = 3 × 16 × 2 = 3 × 4 × 2 = 12 2 Third term, 4 18 = 4 × 9 × 2 = 4 × 3 × 2 = 12 2 Now, 2 50 × 3 32 × 4 18 = 10 2 × 12 2 × 12 2 = 2 × 10 × 12 × 12 = 2 × 1440 So, 2 50 × 3 32 × 4 18 = 1440 2 Hence, the required answer is as shown above.