If √3 = 1.732, then find the value of
(i) √27 + √75 + √108 – √243
(ii) 5√12 – 3√48 + 6√75 + 7√108
Solution:
(i)√27 + √75 + √108 – √243
Let us simplify the expression,
√27 + √75 + √108 – √243
= √(9×3) + √(25×3) + √(36×3) – √(81×3)
= √9 √3 + √25 √3 + √36 √3 – √81 √3
= 3√3 + 5√3 + 6√3 – 9√3
= (3 + 5 + 6 – 9) √3
= 5√3
= 5 × 1.732
= 8.660
(ii)5√12 – 3√48 + 6√75 + 7√108
Let us simplify the expression,
5√12 – 3√48 + 6√75 + 7√108
= 5√(4×3) – 3√(16×3) + 6√(25×3) + 7√(36×3)
= 5√4 √3 – 3√16 √3 + 6√25 √3 + 7√36 √3
= 5.2√3 – 3.4√3 + 6.5√3 + 7.6√3
= 10√3 – 12√3 + 30√3 + 42√3
= (10 – 12 + 30 + 42) √3
= 70√3
= 70 × 1.732
= 121.24
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