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Answers − Reducing Surds

1. Reduce the surd √28

2. Simplify the surd √108

3. Reduce the surd √324

(a)		List the perfect squares
		4 9 25 36 49 64 81
(b)		From (a) the GREEN ones below are factors of 324
		4 9 25 36 49 64 81
(c)		From (b) choose the largest perfect square 81
(d)		Carry on as before

	√324	=	√(81 × 4) = 9√4
		=	9 × 2 = 18

4. Simplify the surd √396

(a)		List the perfect squares
		4 9 25 36 49 64 81
(b)		From (a) the GREEN ones below are factors of 396
		4 9 25 36 49 64 81
(c)		From (b) choose the largest perfect square 36
(d)		Carry on as before

	√396	=	√(36 × 11)
		=	6√11

5. Reduce the surd √900

(a)		List the perfect squares
		4 9 25 36 49 64 81 100
(b)		From (a) the GREEN ones below are factors of 900
		4 9 25 36 49 64 81 100
(c)		From (b) choose the largest perfect square 100
(d)		Carry on as before

	√900	=	√(100 × 9)
		=	10√9 = 10 × 3 = 30

6. Simplify the surd √960

(a)		List the perfect squares
		4 9 25 36 49 64 81
(b)		From (a) the GREEN ones below are factors of 960
		4 9 25 36 49 64 81
(c)		From (b) choose the largest perfect square 64
(d)		Carry on as before

	√960	=	√(64 × 15)
		=	8√15

7. Reduce the surd √5120

(a)		List the perfect squares
		4 9 25 36 49 64 81
(b)		From (a) the GREEN ones below are factors of 5120
		4 9 25 36 49 64 81
(c)		From (b) choose the largest perfect square 64
(d)		Carry on as before

	√5120	=	√(64 × 80) = 8√80
		=	8√(4 × 20) = 8.2√20
		=	16√(4 × 5) = 16.2√5
		=	32√5

8. Simplify the surd √3675

(a)		List the perfect squares
		4 9 25 36 49 64 81
(b)		From (a) the GREEN ones below are factors of 3675
		4 9 25 36 49 64 81
(c)		From (b) choose the largest perfect square 49
(d)		Carry on as before

	√3675	=	√(49 × 75) = 7√75
		=	7√(25 × 3) = 7.5√3
		=	35√3

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