Question
Rationales the denominator and simplify:$\frac{2\sqrt6-\sqrt5}{3\sqrt5-2\sqrt6}$
✓
Answer
$\frac{2\sqrt6-\sqrt5}{3\sqrt5-2\sqrt6}$Rationalizing the denominator by multiplying both numerator and denominator with the rationalizing factor $3\sqrt5+2\sqrt6$
$=\frac{\big(2\sqrt6-\sqrt5\big)\big(3\sqrt5+2\sqrt6\big)}{\big(3\sqrt5-2\sqrt6\big)\big(3\sqrt5+2\sqrt6\big)}$
As we know, $(\text{a}-\text{b})(\text{a}-\text{b})=(\text{a}^2-\text{b}^2)$
$=\frac{\big(2\sqrt6-\sqrt5\big)\big(3\sqrt5+2\sqrt6\big)}{45-24}$
$=\frac{\big(2\sqrt6-\sqrt5\big)\big(3\sqrt5+2\sqrt6\big)}{21}$
$=\frac{6\sqrt{30}+24-15-2\sqrt{30}}{21}$
$=\frac{4\sqrt{30}+9}{21}$
$=\frac{\big(2\sqrt6-\sqrt5\big)\big(3\sqrt5+2\sqrt6\big)}{\big(3\sqrt5-2\sqrt6\big)\big(3\sqrt5+2\sqrt6\big)}$
As we know, $(\text{a}-\text{b})(\text{a}-\text{b})=(\text{a}^2-\text{b}^2)$
$=\frac{\big(2\sqrt6-\sqrt5\big)\big(3\sqrt5+2\sqrt6\big)}{45-24}$
$=\frac{\big(2\sqrt6-\sqrt5\big)\big(3\sqrt5+2\sqrt6\big)}{21}$
$=\frac{6\sqrt{30}+24-15-2\sqrt{30}}{21}$
$=\frac{4\sqrt{30}+9}{21}$
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 given figure, O is the canter of the circle and $\angle\text{AOB}=70^\circ.$ Calculate the values of
→- $\angle\text{OCA}$
- $\angle\text{OAC}$
If $\frac{a}{b}=\frac{2}{3}$, then find the values of the following expressions : $\frac{7 b-4 a}{7 b+4 a}$
→In the given figure $\triangle\text{ABC}$ is an isosceles triangle in which AB = AC and a circle passing through B andC intersects AB and AC at D and E respectively. Prove that DE || BC.
→If $3 x-2 y=11$ and $x y=12$, find the value of $27 x^3-8 y^3$
→Factorise:$\sqrt{5}\text{x}^2+2\text{x}-3\sqrt{5}$
→Give the geometric representations of the following equations:
- On the number line.
- On the Cartesain plane.
Prove the Theorem : The sum of any two sides of a triangle is greater than the third side.
The inner diameter of a cylindrical wooden pipe is $24cm$ and its outer diameter is 28cm. The length of the pipe is $35cm.$ Find the mass of the pipe, if $1cm^3$ of wood has a mass of $0.6gm.$
→In Fig. AB || DE Find $\angle\text{ACD}.$
→Observe figure 3.4 and find the measures of ∠PRS and ∠RTS.
