PROPERTIES OF SQUARE ROOTS WORKSHEET

1. Simplify : √6  √3

2. Simplify : 3√8  2√6

3. Simplify : √35 ÷ √7

4. Simplify : 4√27 ÷ 3√3

5. Simplify : 3√425 + 4√68

6. Simplify : √243 - 5√12 + √27 

7. If a = 1/5, then find the value of a. 

8. If (√4)7 ⋅ (√2)-4 = 2k, then solve for k. 

1. Answer :

= √6  √3

= √(6  3)

= √(2  3  3)

= 3√2

2. Answer :

= 3√8  2√6

= (3 ⋅ 2)(√8  √6)

= 6√(8  6)

= 6√(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3)

= 24√6

3. Answer :

= √35 ÷ √7

= √(35/7)

5

4. Answer :

4√27 ÷ 3√3

= (4/3)√(27/3)

= (4/3)(√9)

= (4/3)(3)

= 4

5. Answer :

Decompose 425 and 68 into prime factors using synthetic division. 

√425 = √(5 ⋅ 5 ⋅ 17)

√425 = 5√17

√68 = √(2 ⋅ 2 ⋅ 17)

√68 = 2√17

3√425 + 4√68 : 

= 3(5√17) + 4(2√17)

= 15√17 + 8√17

= 23√17

6. Answer : 

Decompose 243, 12 and 27 into prime factors using synthetic division. 

√243 = √(3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3) = 9√3

√12 = √(2 ⋅ 2 ⋅ 3) = 2√3

√27 = √(3 ⋅ 3 ⋅ 3) = 3√3

√243 - 5√12 + √27 : 

= 9√3 - 5(2√3) + 3√3

= 9√3 - 10√3 + 3√3

= 2√3

7. Answer : 

a = 1/5

a = (1/5)2

a = 12/52

a = 1/25

8. Answer : 

 (√4)7 ⋅ (√2)-4 = 2k

27 ⋅ (21/2)-4 = 2k

27 ⋅ 2-2 = 2k

27 - 2 = 2k

25 = 2k

k = 5

Apart from the stuff given aboveif you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Multiplicative Inverse Worksheet

    Jan 19, 22 09:34 AM

    Multiplicative Inverse Worksheet

    Read More

  2. Multiplicative Inverse

    Jan 19, 22 09:25 AM

    Multiplicative Inverse - Concept - Examples

    Read More

  3. Graphing Linear Functions Worksheet

    Jan 19, 22 08:24 AM

    Graphing Linear Functions Worksheet

    Read More