Question

rationalize 1/3+2 root 2

Answer 1

$1 \div 3 + 2 \sqrt{2} \\ 3 - 2 \sqrt{2} \div 3 + 2 \sqrt{2} \times 3 - 2 \sqrt{2} \\ 3 - 2 \sqrt{2} \div 9 - 8 \\ 3 - 2 \sqrt{2}$

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Answer 2

The rationalization of  1 / (3 +2√2) is 3 -2√2.

Given:

1 / (3 +2√2)

To Find:

The rationalization of the given number.

Solution:

Rationalization is the process used to eliminate an imaginary number from the denominator of an algebraic fraction.

To rationalize the given number multiply and divide by 3 -2√2 to the number.

$\frac{1}{3 +2\sqrt{2} } * \frac{3 -2\sqrt{2}}{3 -2\sqrt{2}} \\\\= \frac{3 -2\sqrt{2}}{(3 +2\sqrt{2})(3 -2\sqrt{2})}$

(A+B)(A-B) = A² -B²

Here A= 3  and B= 2√2

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

$= \frac{3 - 2\sqrt{2} }{9 - 8} \\\\=\frac{3 - 2\sqrt{2} }{1}\\\\ = 3 - 2\sqrt{2}$

∴ The rationalization of  1 / (3 +2√2) is 3 -2√2

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