Question

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29. Write three radical expressions that have 4√2s as their simplified form. What do the three expressions have in common, explain.

30. The width of a triangle is s. its length is 3s. How long is a diagonal of the rectangle ? Express your answer in simplified radical form.

Answer 1

29.

1) √32 = √(16*2) = 4√2

2) √64 / √2 = 8 /√2 = 8 *√2 / (√2 * √2) = 8√2 / 2 = 4√2

3) 2√8  = 2√(4*2) = 2*2 √2 = 4√2

All the original expressions have to content √2, which cannot be simplified.

30. w = s
       l = 3s

diagonal = hypotenuse = h

h ^2 = w^2 + l^2

h^2 = s^2 + (3s)^2 = s^2 + 9s^2 = 10s^2

h = √(10s^2) = s√5

Answer: diagonal = s√5