Question

simplify 1 upon root 24 - 2 root 135 - root 15 ​

Answer 1

simplest form will be {√6 - 84√(15)}/12

it is given that,

1/√24 - 2√(135) - √15

= 1/√(2 × 2 × 2 × 3) - 2/√(3 × 3 × 3 × 5) - √(15)

= 1/√(2² × 6) - 2√(3² × 15) - √(15)

= 1/2√6 - 2 × 3√15 - √15

= 1/2√6 - 6√15 - √15

= 1/2√6 - 7√15

= (1 - 7√15 × 2√6)/2√6

= {1- 14√(15 × 6)}/2√6

= {1 - 14√(2 × 3 × 3 × 5)}/2√6

= {1 - 42√(10)}/2√6

now rationalising,

= {1 - 42√10}/2√6 × √6/√6

= {√6 - 42√(10 × 6)}/12

= {√6 - 42√(60)}/12

= {√6 - 42√(2 × 2 × 15)}/12

= {√6 - 84√(15)}/12

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Answer 2

The Answer is $\frac{\sqrt{6}-84\sqrt{15} }{12}$

Step-by-step explanation:

Given,

Simplify:  $\frac{1}{\sqrt{24}}-2\sqrt{135}-\sqrt{15}$

∴ $\frac{1}{\sqrt{24}}-2\sqrt{135}-\sqrt{15}$

$=\frac{1}{\sqrt{2\times 2\times 2\times 3} } -2\sqrt{3\times 3\times 3\times 5}-\sqrt{3\times 5}$

$=\frac{1}{2\sqrt{6}}-(2\times 3)\sqrt{15}-\sqrt{15}$

$=\frac{1}{2\sqrt{6}}-6\sqrt{15}-\sqrt{15}$

$=\frac{1}{2\sqrt{6}}-7\sqrt{15}$

$=\frac{1-14\sqrt{90} }{2\sqrt{6} }$

$=\frac{1-42\sqrt{10} }{2\sqrt{6} }$

$=\frac{(1-42\sqrt{10})\sqrt{6}}{2\sqrt{6}\times \sqrt{6} }$

$=\frac{\sqrt{6}-42\sqrt{60} }{12}$

$=\frac{\sqrt{6}-84\sqrt{15} }{12}$

So, The Answer is $\frac{\sqrt{6}-84\sqrt{15} }{12}$