Question
Write a pair of irrational numbers whose sum is irrational.
✓
Answer
$(\sqrt{3}+5)$ and $(\sqrt{5}-3)$ are irrational numbers whose sum is irrational.
Thus, we have
$(\sqrt{3}+5)+(\sqrt{5}-3) $
$=\sqrt{3}+5+\sqrt{5}-3$
$=\sqrt{3}+\sqrt{5}+2,$
which is irrational.
Thus, we have
$(\sqrt{3}+5)+(\sqrt{5}-3) $
$=\sqrt{3}+5+\sqrt{5}-3$
$=\sqrt{3}+\sqrt{5}+2,$
which 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.
Explore more
Similar questions
In the adjoining figure, ABCD is a trapezium in which $AB \| DC$ and E is the mid-point of AD . If $EF \| AB$ meets BC at F , show that F is the mid-point of BC .
→Two figures are similar. If the ratio of their perimeters is $8:16.$ What will be the ratio of the corresponding sides?
→If $\log _{\sqrt{27}} x=2 \frac{2}{3},$ find $x$
→In $\triangle ABC, AB = AC, BM$ and $Cn$ are perpendiculars on $AC$ and $AB$ respectively. Prove that $BM = CN.$
→Find three rational numbers between:-1 and 1
In a polygon, there are $3$ right angles and the remaining angles are equal to $165^\circ .$ Find the number of sides in the polygon.
→A rectangle $\text{PQRS}$ is drawn on the coordinate axes such that $P$ is the origin, $PQ = 6$ units and $PS = 5$ units. Find the coordinates of the vertices $P, Q R$ and $S.$ Also, find the area of the rectangle.
→In the given figure, two chords AC and BD of a circle intersect at E. If arc AB are CD, prove that BE = EC and AE = ED.
For the equation given below, find the slope and the $y-$intercept:$x= 5y - 4$
→A fraction becomes $\frac{1}{2}$ when 1 is subtracted from its numerator and 1 is added to its denominator. Also, it becomes $\frac{1}{3}$ when 6 is subtracted from its numerator and 1 from the denominator. Find the original fraction.
→