Skip to main content
Evaluate
Tick mark Image

Similar Problems from Web Search

Share

\frac{\sqrt{2}}{\sqrt{3}+2\sqrt{2}}
Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.
\frac{\sqrt{2}\left(\sqrt{3}-2\sqrt{2}\right)}{\left(\sqrt{3}+2\sqrt{2}\right)\left(\sqrt{3}-2\sqrt{2}\right)}
Rationalize the denominator of \frac{\sqrt{2}}{\sqrt{3}+2\sqrt{2}} by multiplying numerator and denominator by \sqrt{3}-2\sqrt{2}.
\frac{\sqrt{2}\left(\sqrt{3}-2\sqrt{2}\right)}{\left(\sqrt{3}\right)^{2}-\left(2\sqrt{2}\right)^{2}}
Consider \left(\sqrt{3}+2\sqrt{2}\right)\left(\sqrt{3}-2\sqrt{2}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{\sqrt{2}\left(\sqrt{3}-2\sqrt{2}\right)}{3-\left(2\sqrt{2}\right)^{2}}
The square of \sqrt{3} is 3.
\frac{\sqrt{2}\left(\sqrt{3}-2\sqrt{2}\right)}{3-2^{2}\left(\sqrt{2}\right)^{2}}
Expand \left(2\sqrt{2}\right)^{2}.
\frac{\sqrt{2}\left(\sqrt{3}-2\sqrt{2}\right)}{3-4\left(\sqrt{2}\right)^{2}}
Calculate 2 to the power of 2 and get 4.
\frac{\sqrt{2}\left(\sqrt{3}-2\sqrt{2}\right)}{3-4\times 2}
The square of \sqrt{2} is 2.
\frac{\sqrt{2}\left(\sqrt{3}-2\sqrt{2}\right)}{3-8}
Multiply 4 and 2 to get 8.
\frac{\sqrt{2}\left(\sqrt{3}-2\sqrt{2}\right)}{-5}
Subtract 8 from 3 to get -5.
\frac{\sqrt{2}\sqrt{3}-2\left(\sqrt{2}\right)^{2}}{-5}
Use the distributive property to multiply \sqrt{2} by \sqrt{3}-2\sqrt{2}.
\frac{\sqrt{6}-2\left(\sqrt{2}\right)^{2}}{-5}
To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.
\frac{\sqrt{6}-2\times 2}{-5}
The square of \sqrt{2} is 2.
\frac{\sqrt{6}-4}{-5}
Multiply -2 and 2 to get -4.
\frac{-\sqrt{6}+4}{5}
Multiply both numerator and denominator by -1.