Question

# How many of the given following are surds ?(i) 3√7 (ii) 4√0.16 (iii) 3√√8(iv) √−5 (v) 1√0.16 (vi) √0.333(vii) √576 (viii) √54 (ix) √227 (x) 3√2√9.

A
6
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B
7
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C
8
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D
9
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Solution

## The correct option is D 7(i)3√7 cannot simplified to remove root.(ii) 4√0.16=4√(.4)2=√.4 cannot simplified to remove root.(iii) 3√√8=3√√(2)3=√2 cannot simplified to remove root.(iv) √−5=√5i is a complex number.(v) 1√0.16=√10016=104=2.5 is not a surd, as it is rational.(vi) √0.333 cannot simplified to remove root.(vii) √576=24, which is not a surd, as it is rational.(viii) √54 =√52cannot simplified to remove root.(ix) √227 cannot simplified to remove root.(x) 3√2√9 3√2×3 cannot simplified to remove root. Hence, 3 numbers are not surds. Remaining 7 numbers are surds.Therefore, option C is correct.

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