Name: Mathematical Operations on Exponential Numbers
Uploaded: 2019-07-19
Duration: 6 min 37 s
Description: In this video, we will learn the operations on exponential numbers, such as addition, subtraction, multiplication and division, in a detailed manner.

Question

Show that

\frac{1}{4 - \sqrt{15}} - \frac{1}{\sqrt{15} - \sqrt{14}} + \frac{1}{\sqrt{14} - \sqrt{13}} - \sqrt{13} = 4

Accepted Answer

To prove- $\frac{1}{4 - \sqrt{15}} - \frac{1}{\sqrt{15} - \sqrt{14}} + \frac{1}{\sqrt{14} - \sqrt{13}} - \sqrt{13} = 4$

LHS $= \frac{1}{4 - \sqrt{15}} - \frac{1}{\sqrt{15} - \sqrt{14}} + \frac{1}{\sqrt{14} - \sqrt{13}} - \sqrt{13}$

Multiply and divide the given expression by the least rationalising factor of its denominator.
$\frac{1}{4 - \sqrt{15}} = \frac{1}{4 - \sqrt{15}} \times \frac{4 + \sqrt{15}}{4 + \sqrt{15}} = \frac{4 + \sqrt{15}}{16 - 15} = 4 + \sqrt{15}$
$\frac{1}{\sqrt{15} - \sqrt{14}} = \frac{1}{\sqrt{15} - \sqrt{14}} \times \frac{\sqrt{15} + \sqrt{14}}{\sqrt{15} + \sqrt{14}} = \frac{\sqrt{15} + \sqrt{14}}{15 - 14} = \sqrt{15} + \sqrt{14}$
$\frac{1}{\sqrt{14} - \sqrt{13}} = \frac{1}{\sqrt{14} - \sqrt{13}} \times \frac{\sqrt{14} + \sqrt{13}}{\sqrt{14} + \sqrt{13}} = \frac{\sqrt{14} + \sqrt{13}}{14 - 13} = \sqrt{14} + \sqrt{13}$
Now, according to the question,

$\frac{1}{4 - \sqrt{15}} - \frac{1}{\sqrt{15} - \sqrt{14}} + \frac{1}{\sqrt{14} - \sqrt{13}} - \sqrt{13} = 4 + \sqrt{15} - \sqrt{15} - \sqrt{14} + \sqrt{14} + \sqrt{13} - \sqrt{13}$
$= 4 = R H S$
Hence proved.

Show that $\frac{1}{4 - \sqrt{15}} - \frac{1}{\sqrt{15} - \sqrt{14}} + \frac{1}{\sqrt{14} - \sqrt{13}} - \sqrt{13} = 4$

Important Questions on Number System

Learn and Prepare for any exam you want !

Show that 14-15-115-14+114-13-13=4

Important Questions on Number System

Learn and Prepare for any exam you want !

Show that $\frac{1}{4 - \sqrt{15}} - \frac{1}{\sqrt{15} - \sqrt{14}} + \frac{1}{\sqrt{14} - \sqrt{13}} - \sqrt{13} = 4$