find five rational number between ✓5/7 and 4/9.
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MATHS NUMBER SYSTEM CLASS 9
Selvi T. asked • 07/02/18
insert 5 rational numbers between root 5/7 and 4/9
how to find rational numbers between root of 5 divided by 7 and 4 divided by 7
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Tracey M. answered • 07/02/18
BBA in Actuarial Science ,33+ years as math tutor, Assoc Sociey of Act
Good morning Selvi,
Could you verify that the two values are √5/7 and 4/9. I don't think it makes sense any other way.
√5/7 < x < 4/9
square everything
5/49 < x2 < 16/81
get a common denominator for the endvalues so we can compare them
405/3969 < x2 < 784/3969
Choose 5 numbers between 405 and 784 that are perfect squares.
x2 = 441/3969, 484/3969, 529/3969, 576/3969, 625/3969
x = 21/63 ( which reduces to 1/3), 22/63, 23/63, 24/63, 65/63