Question

rationalise the factor of 1/2√3-5

please explain by step by step​

Answer 1

Answer:

We rationalize the factor of 1/2√3-5

1/2√3-5 × 2√3 + 5 / 2√3+5

2√3+5 / (2√3-5) (2√3+5)

2√3+5 / (2√3)² - (5)² = 2√3+5 / 1

therefore,, answer is 2√3+5

Answer 2

Answer:

$\frac{ - 2 \sqrt{3} + 5 }{13}$

Step-by-step explanation:

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

(now if In denominator we are given a+b then we have to multiply the denominator and numerator. both by a-b and if we are given a-b we have to multiply by a+b .. it is done in order to get (a+b)(a-b) which is expanded form of

${a}^{2} - {b}^{2}$

so here we will multiply by 2 root 3 +5 both in numerator and denominator

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

$\frac{2 \sqrt{3} + 5 }{ { (2\sqrt{3}) }^{2} - {5}^{2} }$

$\frac{2 \sqrt{3 } + 5}{(2 \times 2 \times 3) - 5 \times 5}$

$\frac{2 \sqrt{3} + 5 }{12 - 25}$

$\frac{2 \sqrt{3} + 5}{ - 13}$

$\frac{ - (2 \sqrt{3} + 5}{13}$

$\frac{ - 2 \sqrt{3} + 5 }{13}$

this is your answer cause we have to bring denominator to a natural no.

Hope it helps : )