Simplify- 5-105-10-5-105-10-5-

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Byju's Answer

Standard VIII

Mathematics

Finding Square Root of a Number

Simplify: 5-√...

Question

Simplify: $\frac{5 - \sqrt{10}}{5 + \sqrt{10}} - \frac{5 + \sqrt{10}}{5 - \sqrt{10}}$
$[5]$

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Solution

$\frac{5 - \sqrt{10}}{5 + \sqrt{10}} - \frac{5 + \sqrt{10}}{5 - \sqrt{10}}$

Multiplying both numerator and denominator by the rationalising factor of the denominators, we have

$= \frac{5 - \sqrt{10}}{5 + \sqrt{10}} \times \frac{5 - \sqrt{10}}{5 - \sqrt{10}} - \frac{5 + \sqrt{10}}{5 - \sqrt{10}} \times \frac{5 + \sqrt{10}}{5 + \sqrt{10}}$
$[2]$
$= \frac{(5 - \sqrt{10})^{2}}{25 - \sqrt{(10)^{2}}} - \frac{(5 + \sqrt{10})^{2}}{25 - \sqrt{(10)^{2}}}$

$= \frac{25 - 10 \sqrt{10} + 10}{15} - \frac{25 + 10 \sqrt{10} + 10}{15}$
$[2]$
$= \frac{25 - 10 \sqrt{10} + 10 - 25 - 10 \sqrt{10} - 10}{15}$

$= - \frac{20 \sqrt{10}}{15}$

$= - \frac{4}{3} \sqrt{10}$
$[1]$

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Similar questions

Simplify:

(i) $\frac{25 \times t^{- 4}}{5^{- 3} \times 10 \times t^{- 8}}$

(ii)

\frac{3^{- 5} \times 10^{- 5} \times 125}{5^{- 7} \times 6^{- 5}}

Simplify.(i) $\frac{25 \times t^{- 4}}{5^{- 3} \times 10 \times t^{- 8}}, t \neq 0$ , (ii) $\frac{3^{- 5} \times 10^{- 5} \times 125}{5^{- 7} \times 6^{- 5}}$

Q. Simplify:

(4) (–5) × (–13) + (–5) × 10

Simplify $\frac{5 - \sqrt{10}}{5 + \sqrt{10}}$ - $\frac{5 + \sqrt{10}}{5 - \sqrt{10}}$

Q. Simplify :

[{(- 5)^{5} \times (- 5)^{- 10}} \div 2^{5}] \times 10^{5}

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Simplify: 5−√105+√10−5+√105−√10 [5]

Simplify: $\frac{5 - \sqrt{10}}{5 + \sqrt{10}} - \frac{5 + \sqrt{10}}{5 - \sqrt{10}}$
$[5]$