Question

simplyfy by rationalising the denominator 1/5+2√6​

Answer 1

Answer:

1/5+2√6

→ 1/(5+2√6) ×(5-2√6) /(5-2√6)

→ (5-2√6) /5(5-2√6) +2√6(5-2√6)

→ 5-2√6/25-10√6+10√6-4√6

→ 5-2√6/25-4√6

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

Given

$\bf \frac{1}{5 + 2 \sqrt{6} }$

Rationalising factor of a + b√c = a - b√c.

So, the rationalising factor of 5+2√6 = 5-2√6.

On rationalising the denominator them.

$\rm \longrightarrow \: \frac{1}{5 + 2 \sqrt{6} } \times \frac{5 - 2 \sqrt{6} }{5 - 2 \sqrt{6} }$

$\rm \longrightarrow \: \frac{1( 5 - 2 \sqrt{6} )}{(5 + 2 \sqrt{6})(5 - 2 \sqrt{6} ) }$

Remaimber: Anything multiply by 1 gives itself.

$\rm \longrightarrow \: \frac{5 - 2 \sqrt{6} }{(5 + 2 \sqrt{6} )(5 - 2 \sqrt{6} )}$

• (a + b)(a - b) = a² - b²

• Where, a = 5 and b = 2√6.

$\rm \longrightarrow \: \frac{5 - 2 \sqrt{6} }{(5 {)}^{2} - (2 \sqrt{6} {)}^{2} }$

$\rm \longrightarrow \: \frac{5 - 2 \sqrt{6} }{25 - (2 \sqrt{6} {)}^{2} }$

$\rm \longrightarrow \: \frac{5 - 2 \sqrt{6} }{25 - {2}^{2} ( \sqrt{6 } {)}^{2} }$

$\rm \longrightarrow \: \frac{5 - 2 \sqrt{6} }{25 - 4 \times 6}$

$\rm \longrightarrow \: \frac{5 - 2 \sqrt{6} }{25 - 24}$

$\rm \longrightarrow \: \frac{5 - 2 \sqrt{6} }{1}$

Remaimber: Anything divided by one gives itself.

$\bf \longrightarrow \: 5 - 2 \sqrt{6}$

$\bf \: Hence, the \: denominator \: is \: rationalised.$

• I hope it's help you.☺