Question

Solve these rationalism 1/2√2-5√3​

Answer 1

Correct Question:

Solve these by rationalisation -

$\bf \dfrac{1}{2\sqrt{2} - 5\sqrt{3}}$

Given:

The expression -

$\bf \dfrac{1}{2\sqrt{2} - 5\sqrt{3}}$

What To Find:

We have to -

• Rationalise the denominator.

Solution:

Here the rationalising factor of the denominator is -

$\sf \implies 2\sqrt{2} + 5\sqrt{3}$

Multiply the rationalising factor with the expression,

$\sf \implies \dfrac{1}{2\sqrt{2} - 5\sqrt{3}} \times \dfrac{2\sqrt{2} + 5\sqrt{3}}{2\sqrt{2} + 5\sqrt{3}}$

Solve the numerator,

$\sf \implies \dfrac{2\sqrt{2} + 5\sqrt{3}}{2\sqrt{2} - 5\sqrt{3} \times 2\sqrt{2} + 5\sqrt{3}}$

Solve the denominator by using the identity (a + b) (a - b) = a² - b²,

Where,

• a = 2√2
• b = 5√3

$\sf \implies \dfrac{2\sqrt{2} + 5\sqrt{3}}{(2\sqrt{2})^2 - (5\sqrt{3})^2}$

Solve the brackets,

$\sf \implies \dfrac{2\sqrt{2} + 5\sqrt{3}}{(2 \times 2 \times \sqrt{2} \times \sqrt{2}) - (5 \times 5 \times \sqrt{3} \times \sqrt{3})}$

Solve the brackets further,

$\sf \implies \dfrac{2\sqrt{2} + 5\sqrt{3}}{8 - 75}$

Subtract 75 from 8,

$\sf \implies \dfrac{2\sqrt{2} + 5\sqrt{3}}{-67}$

Also written as,

$\sf \implies -\dfrac{2\sqrt{2} + 5\sqrt{3}}{67}$

Final Answer:

∴ Thus, the answer is $\sf -\dfrac{2\sqrt{2} + 5\sqrt{3}}{67}$ after rationalising the denominator.