six students (A,B,C,D,E and F) of grade 7 ran the fallowing distances in kilometers in 2 hours:4√2,2√3,3√2,√17,3√3,and 5,respectively.arrange the distances in increasing order on a number line.who ran the fastest?
paki sagotan poh
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six students (A,B,C,D,E and F) of grade 7 ran the fallowing distances in kilometers in 2 hours:4√2,2√3,3√2,√17,3√3,and 5,respectively.arrange the distances in increasing order on a number line.who ran the fastest?
paki sagotan poh
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Solution :
Key Concept :
Most of the given distances are irrational numbers.
So, square the given distances and order them from least to greatest.
Step 1 :
Take square to 4√2.
(4√2)2 = (4)2(√2)2
(4√2)2 = (16)(2)
(4√2)2 = 32 -----(A)
Step 2 :
Take square to 2√3.
(2√3)2 = (2)2(√3)2
(2√3)2 = (4)(3)
(2√3)2 = 12 -----(B)
Step 3 :
Take square to 3√2.
(3√2)2 = (3)2(√2)2
(3√2)2 = (9)(2)
(3√2)2 = 18 -----(C)
Step 4 :
Take square to √17.
(√17)2 = 17 -----(D)
Step 5 :
Take square to 3√3.
(3√3)2 = (3)2(√3)2
(3√3)2 = (9)(3)
(3√3)2 = 27 -----(E)
Step 6 :
Take square to 5.
(5)2 = 25 -----(F)
Step 7 :
Comparing (A), (B), (C), (D), (E) and (F), student A ran the farthest distance.
And also, from (A), (B), (C), (D), (E) and (F), we can write the squares of the given distances from least to greatest as given below.
12, 17, 18, 25, 27, 32
In the above order, write the corresponding distance to its square to write the given distances in the order from least to greatest.
2√3 km, √17 km, 3√2 km, 5 km, 3√3 km, 4√2 km
Hence, the order of the students by distance covered by them from least to greatest is
B, D, C, F, E, A