Selina Solutions Class 9 Mathematics Solutions for Exercise 1(B) in Chapter 1 - Chapter 1- Rational and Irrational Numbers

Question 5 Exercise 1(B)

Use method of contradiction to show that √𝟑 and √𝟓 are irrational.


Let us suppose that √3 and √5 are rational numbers

√3 = a/b

and √5 = x/y

(Where a, b \epsilon and b, y \ne0 x , y)

Squaring both sides

\begin{array}{ll} 3=\frac{a^{2}}{b^{2}} & , 5=\frac{x^{2}}{y^{2}} \\ 30^{2}=a^{2} & \left., 5 y^{2}=x^{2}\right\} \quad \ldots(*) \end{array}

a² and x² are odd as 3b² and 5y² are odd .

a and x are odd....(1)

Let a = 3c, x = 5z

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