Question
Rationalize the denominator : $\frac{4}{7+4 \sqrt{3}}$
✓
Answer
$ \frac{4}{7+4 \sqrt{3}}= \frac{4}{(7+4 \sqrt{3})} \times \frac{(7-4 \sqrt{3})}{(7-4 \sqrt{3})}$
$\ldots[\text { Multiplying the numerator and }$
$\text { denominator by }(7-4 \sqrt{3})]$
$= \frac{4(7-4 \sqrt{3})}{(7)^2-(4 \sqrt{3})^2}$
$= \frac{4(7-4 \sqrt{3})}{49-(16 \times 3)}$
$= \frac{4(7-4 \sqrt{3})}{49-48}=\frac{4(7-4 \sqrt{3})}{1}$
$\therefore \quad \frac{4}{7+4 \sqrt{3}}= 28-16 \sqrt{3}$
$\ldots[\text { Multiplying the numerator and }$
$\text { denominator by }(7-4 \sqrt{3})]$
$= \frac{4(7-4 \sqrt{3})}{(7)^2-(4 \sqrt{3})^2}$
$= \frac{4(7-4 \sqrt{3})}{49-(16 \times 3)}$
$= \frac{4(7-4 \sqrt{3})}{49-48}=\frac{4(7-4 \sqrt{3})}{1}$
$\therefore \quad \frac{4}{7+4 \sqrt{3}}= 28-16 \sqrt{3}$
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
Solve the following equations for x:$2^{\text{2x}}-2^{\text{x}+3}+2^4=0$
→Divide $x^4 - 5x^2 - 4x by x + 3$ and find the remainder(using reminder theorem).
→Simplify:$\frac{\sqrt5+\sqrt3}{\sqrt5-\sqrt3}+\frac{\sqrt5-\sqrt3}{\sqrt5+\sqrt3}$
→The circumference of the base of a $10m$ height conical tent is $44m$, calculate the length of canvas used in making the tent if width of canvas is $2m$ $\Big($Use $\pi=\frac{22}{7}\Big).$
→Evaluate the following using identities:
$991 \times 1009$
→$991 \times 1009$
From the given figure, name the following:
- Three lines.
- One rectilinear figure.
- Four concurrent points.
Find the angle whose supplement is four times its complement.
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface areas.
Solve 8x + 3y = 11 ; 3x – y = 2
Factorise:
$7(x - 2y)^2 - 25(x - 2y) + 12$
→$7(x - 2y)^2 - 25(x - 2y) + 12$