**Multiplying radical expressions worksheet :**

Here we are going to see some practice questions multiplying radical expressions.

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.

(1) Multiply the radical expression given below

√6 (√3 + √12)

(2) Multiply the radical expression given below

(√2 + √7) (√5 - √6)

(3) Multiply the radical expression given below

(-3√(3x) + 4) (√3x - 5)

(4) Multiply the radical expression given below

(2 - 3√5) (5 - √5)

(5) Multiply the radical expression given below

(5 + 4√3) (3 + √3)

(6) Multiply the radical expression given below

- 4√(28 x) **x **√(7x^3)

(7) Multiply the radical expression given below

√(15x^2) **x **√(10x^3)

(8) Multiply the radical expression given below

√6 **x **√6

(9) Multiply the radical expression given below

3√12 **x **√6

(10) Multiply the radical expression given below

(5√24 +** **√3)(2 - √3)

**Let us see some example problems to understand the concept. **

**Problem 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.

**Problem 2 :**

Multiply the radical expression given below

(√2 + √7) (√5 - √6)

**Solution :**

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

**Problem 3 :**

Multiply the radical expression given below

(-3√(3x) + 4) (√3x - 5)

**Solution :**

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

**Problem 4 :**

Multiply the radical expression given below

(2 - 3√5) (5 - √5)

**Solution :**

**Hence 25 - 13**√5 is the answer.

**Problem 5 :**

Multiply the radical expression given below

(5 + 4√3) (3 + √3)

**Solution :**

**Hence 27 + 17**√3 is the answer.

**Problem 6 :**

Multiply the radical expression given below

- 4√(28 x) **x **√(7x^3)

**Solution :**

**Hence -56 x^2 **is the answer.

**Problem 7 :**

Multiply the radical expression given below

√(15x^2) **x **√(10x^3)

**Solution :**

= √(15x^2) **x **√(10x^3)

= √(15 **x **10 **x **x^2 **x **x^3)

= √(5 **x **3 **x **2 **x **5** **x^2 **x **x^3)

= 5 x^4√(3 **x **2 **x** x)

= 5 x^4√6 x

**Hence** 5 x^4√6 x ** **is the answer.

**Problem 8 :**

Multiply the radical expression given below

√6 **x **√6

**Solution :**

= √6 **x **√6

= 6

Hence 6 is the answer.

**Problem 9 :**

Multiply the radical expression given below

3√12 **x **√6

**Solution :**

= 3√12 **x **√6

= 3√(12 x 6)

= 3√(2 x 2 x 3 x 2 x 3)

= (3 x 2 x 3)√2

= 18√2

Hence 18√2 is the answer.

**Problem 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 - √3√3

= 10(2) - 5√6 + √6 - 3

= 20 - 4√6 - 3

= 17 - 4√6

Hence the answer is 17 - 4√6.

- Properties of radicals
- Simplifying radical expressions worksheets
- Square roots
- Ordering square roots from least to greatest
- Operations with radicals
- How to simplify radical expressions

After having gone through the stuff given above, we hope that the students would have understood "Multiplying radical expressions worksheet".

Apart from the stuff given above, if you want to know more about "Multiplying radical expressions worksheet", please click here

Apart from the stuff "Multiply radical expressions", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**