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Number Theory: Interesting Results

State whether...

Question

State whether True or False :

All the following numbers are irrationals.
(i) $\frac{2}{\sqrt{7}}$ (ii) $\frac{3}{2 \sqrt{5}}$ (iii) $4 + \sqrt{2}$ (iv) $5 \sqrt{2}$

True

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False

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Solution

The correct option is A True
In all of the above questions $\sqrt{7}, \sqrt{5}, \sqrt{2}$ are a $i r r a t i o n a l$ numbers

And $the addition, subtraction, division and product between rational and irrational gives an irrational number$

So that all of the above are irrational numbers.

hence option A is correct.

Suggest Corrections

Similar questions

State, in each case, whether true or false.

$(i) \sqrt{2} + \sqrt{3} = \sqrt{5}$

$(i i) 2 \sqrt{4} + 2 = 6$

$(i i i) 3 \sqrt{7} - 2 \sqrt{7} = \sqrt{7}$

$(i v) \frac{2}{7}$ is an irrational number.

$(v) \frac{5}{11}$ is a rational number.

(vi) All rational numbers are real numbers.

(vii) All real numbers are rational numbers.

(viii) Some real numbers are rational numbers.

State, True or False :

(i) $x < - y \Rightarrow - x > y$

(ii) $- 5 x \geq 15 \Rightarrow x \leq - 3$

(iii) $2 x \leq - 7 \Rightarrow \frac{2 x}{- 4} \geq \frac{- 7}{- 4}$

(iv) $7 > 5 \Rightarrow \frac{1}{7} < \frac{1}{5}$

3 \sqrt[4]{\sqrt[3]{5}} - \sqrt[3]{\sqrt[4]{5}}

= 2 \cdot \sqrt[12]{5}

\frac{2}{5}

\frac{4}{7}

\frac{3}{4}

\frac{1}{2}

\frac{- 2}{3} + 0 = 0 + (\begin{matrix} \frac{- 2}{3} \end{matrix}) = \frac{- 2}{3}

\frac{- 4}{5} + \frac{7}{8} = \frac{7}{8} + (\begin{matrix} \frac{- 4}{5} \end{matrix})

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