Question

Rationalize 8√3/2√18

Answer 1

The solution to your question is in the attachment.

What is rationalization?

Answer :-

• Rationalizing is the process in which an irrational number is converted into its rational form.

For example we can take an example:-

Question:- Rationalize the denominator:-

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

$\frac{ \sqrt{} 3 + \sqrt{2} }{ \sqrt{} 3 - \sqrt{2} } = \frac{ \sqrt{} 3 + \sqrt{2} }{ \sqrt{} 3 - \sqrt{2} } \times \frac{ \sqrt{} 3 + \sqrt{2} }{ \sqrt{} 3 + \sqrt{2} }$

Multiplying both numerator and denominator with the irrational numbers with opposite sign of the denominator of the irrational number on left side of multiplication sign.

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

Now splitting The numerator using the identity (a+b)²=a²+b²+2ab. The denominator is solved by squaring the square roots.

$= \frac{( \sqrt{3}) {}^{2} + ( \sqrt{2} ) {}^{2} + 2 \sqrt{3} \sqrt{2} }{3 - 2} \\ = \frac{3 + 2 + 2 \sqrt{6} }{1} = 5 + 2 \sqrt{6}$

Square of root 3 is 3 and the square of root 2 is 2.