If we want to multiply two radical terms, then first we have to consider whether they are having same order.

Whenever we have two or more radical terms which are multiplied with same index, then we can put only one radical and multiply the terms inside the radical.

Let us see some example problems to understand the concept.

Example 1 :

Multiply the radical expression given below

√6 (√3 + √12)

Solution :

=   3√2 + (2 x 3) √2

=   3√2 + 6 √2

=   (3 + 6)√2

=   9 √2

Hence 9 √2 is the answer.

Example 2 :

Multiply the radical expression given below

(√2 + √7) (√5 - √6)

Solution :

Hence √10 +  √35 - 2√3 + √42 is the answer.

Example 3 :

Multiply the radical expression given below

(-3√(3x) + 4) (√3x - 5)

Solution :

Hence, -9x + 19√3x - 20 is the answer.

Example 4 :

Multiply the radical expression given below

(2 - 3√5) (5 - √5)

Solution :

Hence 25 - 13√5 is the answer.

Example 5 :

Multiply the radical expression given below

(5 + 4√3) (3 + √3)

Solution :

Hence 27 + 17√3 is the answer.

Example 6 :

Multiply the radical expression given below

- 4√(28 x) √(7x^3)

Solution :

Hence -56 x^2 is the answer.

Example 7 :

Multiply the radical expression given below

√(15x^2) √(10x^3)

Solution :

=  √(15x^2) √(10x^3)

=  √(15 10 x^2 x^3)

=  √(5 x x 5 x^2 x^3)

= 5 x^4√(3 x x)

= 5 x^4√6 x

Hence 5 x^4√6  is the answer.

Example 8 :

Multiply the radical expression given below

√6 √6

Solution :

=  √6 √6

=  6

Example 9 :

Multiply the radical expression given below

3√12 √6

Solution :

=  3√12 √6

=  3√(12 x 6)

= 3√(2 x 2 x 3 x 2 x 3)

= (3 x 2 x 3)√2

= 18√2

Example 10 :

Multiply the radical expression given below

(5√24 + √3)(2 - √3)

Solution :

=  (5√2 + √3)(√2 - √3)

=  10√2 √2 - 5√6 + √2√3 - 33

=  10(2) - 5√6 + √6 - 3

=  20 - 4√6 - 3

=  17 - 4√6

Hence the answer is 17 - 4√6.

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