Question

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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1 Expert Answer

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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