Download App

Presentation of Data in Tabular Form — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsPresentation of Data in Tabular Form2 Marks
Question
Examine whether the following numbers are rational or irrational.
$3+\sqrt{3}$
✓

Answer

Let us assume, to the contrary, that $3+\sqrt{3}$ is rational.
Then, $3+\sqrt{3}=\frac{\text{p}}{\text{q}},$ where p and q are coprime and $\text{q}\neq0.$
$\Rightarrow\sqrt{3}=\frac{\text{p}}{\text{q}}-3$
$\Rightarrow\sqrt{3}=\frac{\text{p}-3\text{q}}{\text{q}}$
Since, p and q are are integers.
$\Rightarrow\frac{\text{p}-3\text{q}}{\text{q}}$ is rational.
So, $\sqrt{3}$ is also rational.
But this contradicts the fact that $\sqrt{3}$ is irrational.
This contradiction has arisen because of our incorrect assumption that $3+\sqrt{3}$ is rational.
Hence, $3+\sqrt{3}$ is irrational.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Presentation of Data in Tabular Form→Presentation of Data in Tabular Form — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

Find the mean of first five multiples of 3
→
Multiply:
$\sqrt{10}$ by $\sqrt{40}$
→
Verify $x = - \frac{1}{3}$ are zeroes of the polynomial $p\left( x \right) = 3x + 1$
→

Define cumulative frequency distribution.

→
Verify that:
2 and -3 are the zeros of the polynomial q(x) = x2 + x - 6.
→
Find the mean of:
The first ten odd numbers.
→
ABC is an isosceles triangle with AB = AC. Draw AP $\perp$ BC to show that $\angle$B = $\angle$C.
→
Factorise:
(a + b)3 - a - b
→
Simplify the following:
$\frac{\sqrt{24}}{8}+\frac{\sqrt{54}}{9}$
→
Rationalise the denominator of the following:
$\frac{1}{\sqrt{5}-2}$
→