Question

6√5 is a ____________ surd.

Answer 1

Answer:

√5 × √10

= 5⋅10−−−−√5⋅10

= 5⋅5⋅2−−−−−−√5⋅5⋅2

= 5√2, which is an irrational number.  Hence, it is a surd.

(ii) √8 × √6

= 8⋅6−−−√8⋅6

= 2⋅2⋅2⋅2⋅3−−−−−−−−−−√2⋅2⋅2⋅2⋅3

= 4√3, which is an irrational number.  Hence, it is a surd.

(iii) √27 × √3

= 27⋅3−−−−√27⋅3

= 3⋅3⋅3⋅3−−−−−−−−√3⋅3⋅3⋅3

= 3 × 3

= 9, which is a rational number.  Hence, it is not a surd.

 

(iv) √16 × √4

= 16⋅4−−−−√16⋅4

= 2⋅2⋅2⋅2⋅2⋅2−−−−−−−−−−−−√2⋅2⋅2⋅2⋅2⋅2

= 2 × 2 × 2

= 8, which is a rational number.  Hence, it is not a surd.

(v) 5√8 × 2√6

= 5 × 2 2⋅2⋅2⋅2⋅3−−−−−−−−−−√2⋅2⋅2⋅2⋅3

= 10 × 2 × 2 × √3

= 40√3, which is an irrational number.  Hence, it is a surd.