# 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.

= √6  √3

= √(6  3)

= √(2  3  3)

= 3√2

= 3√8  2√6

= (3 ⋅ 2)(√8  √6)

= 6√(8  6)

= 6√(2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 3)

= 24√6

= √35 ÷ √7

= √(35/7)

5

4√27 ÷ 3√3

= (4/3)√(27/3)

= (4/3)(√9)

= (4/3)(3)

= 4

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

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

a = 1/5

a = (1/5)2

a = 12/52

a = 1/25

(√4)7 ⋅ (√2)-4 = 2k

27 ⋅ (21/2)-4 = 2k

27 ⋅ 2-2 = 2k

27 - 2 = 2k

25 = 2k

k = 5

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