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Question

Find the value of:
(i) 80405
(ii) 441625
(iii) 15871728
(iv) 72×338
(v) 45×20

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Solution

(i) We have:
frac{sqrt{80}}{sqrt{405}}=sqrt{frac{80}{405}}=sqrt{frac{16}{81}}=frac{sqrt{16}}{sqrt{81}}=frac{4}{9}

(ii) Computing the square roots:
sqrt{441}=sqrt{left (3times3 right )timesleft (7times7 right )}=3times7=21
sqrt{625}=sqrt{left (5times5 right )timesleft (5times5 right )}=5times5=25
frac{sqrt{441}}{sqrt{625}}=frac{21}{25}

(iii) We have:

frac{sqrt{1587}}{sqrt{1728}}=sqrt{frac{529}{576}} (by dividing both numbers by 3)
Computing the square roots of the numerator and the denominator:
sqrt{529}=sqrt{23times23}=23
sqrt{576}=sqrt{24times24}=24

frac{sqrt{1587}}{sqrt{1728}}=frac{23}{24}

(iv) We have:
sqrt{72}timessqrt{338} =sqrt{72times338} =sqrt{2times2times2times3times3times2times13times13}
==sqrt{2times2times2times2times3times3times13times13} =2times2times3times13
=156
(v) We have:
sqrt{45}timessqrt{20} = sqrt{3times3times5times2times2times5}
= sqrt{3times3times2times2times5times5}
= 30

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