Question

rationalize the denominator..1/2+✓2 ??​

Answer 1

Answer :

$=\frac{2-\sqrt{2}}{2}$

Step-by-step explanation :

$\underline{\underline{\bf Rationalizing \ factor:}}$

• The factor of multiplication by which rationalization is done, is called as rationalizing factor.

• If the product of two surds is a rational number, then each surd is a rationalizing factor to other.

• To find the rationalizing factor,

         =>  If the denominator contains 2 terms, just change the sign between the two terms.

             For example, rationalizing factor of (3 + √2) is (3 - √2)

         => If the denominator contains 1 term, the radical found in the denominator is the factor.

             For example, rationalizing factor of √2 is √2

____________________________

$\bf =\frac{1}{2+\sqrt{2}}$

Rationalizing factor = 2 - √2

$\bf =\frac{1}{2+\sqrt{2}} \times \frac{2-\sqrt{2} }{2-\sqrt{2}} \\\\\\ =\frac{2-\sqrt{2} }{(2+\sqrt{2})(2-\sqrt{2})} \\\\\\ =\frac{2-\sqrt{2}}{2(2-\sqrt{2})+\sqrt{2}(2-\sqrt{2})} \\\\\\ =\frac{2-\sqrt{2}}{4-2\sqrt{2}+2\sqrt{2}-\sqrt{2}^2} \\\\\\ =\frac{2-\sqrt{2}}{4-2} \\\\\\ =\frac{2-\sqrt{2}}{2} \\\\\\ =1-\frac{\sqrt{2}}{2}$

Answer 2

Step-by-step explanation:

refer the attachment......