Surds

Question 1

What is 4√54 x 2√90

Explain your process!

Answer 1

72√60

4√54 x 2√90
4 x √9 x √6 x 2 x √9 x √10
4 x 3 x √6 x 2 x 3 x √10

Question 2

What is √50 as a surd

Explain your process!

Answer 2

5√2

√50
√25 x √2
5 x √2
5√2

Question 3

What is 4√27 x 3√12

Explain your process!

Answer 3

216

4√27 x 3√12
4 x √9 x √3 x 3 x √3 x √4
4 x 3 x √3 x 3 x √3 x 2 
72 x √9 
72 x 3 = 216

Question 4

What is 1/√6 x 3/√2

Explain your process!

Answer 4

√3/2

1/√6 x 3/√2 = 3/√12
3/√12 x √12/√12 = 3√12/12
3√12/12 = 3 x √4 x √3/12
3 x 2 x √3 = 6√3
6√3/12 = √3/2