Skip to main content
Evaluate
Tick mark Image
Expand
Tick mark Image

Similar Problems from Web Search

Share

\left(\sqrt{5}\right)^{2}+2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}-\sqrt{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{5}+\sqrt{3}\right)^{2}.
5+2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}-\sqrt{3}\right)^{2}
The square of \sqrt{5} is 5.
5+2\sqrt{15}+\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}-\sqrt{3}\right)^{2}
To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.
5+2\sqrt{15}+3-\left(\sqrt{5}-\sqrt{3}\right)^{2}
The square of \sqrt{3} is 3.
8+2\sqrt{15}-\left(\sqrt{5}-\sqrt{3}\right)^{2}
Add 5 and 3 to get 8.
8+2\sqrt{15}-\left(\left(\sqrt{5}\right)^{2}-2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{5}-\sqrt{3}\right)^{2}.
8+2\sqrt{15}-\left(5-2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}\right)
The square of \sqrt{5} is 5.
8+2\sqrt{15}-\left(5-2\sqrt{15}+\left(\sqrt{3}\right)^{2}\right)
To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.
8+2\sqrt{15}-\left(5-2\sqrt{15}+3\right)
The square of \sqrt{3} is 3.
8+2\sqrt{15}-\left(8-2\sqrt{15}\right)
Add 5 and 3 to get 8.
8+2\sqrt{15}-8+2\sqrt{15}
To find the opposite of 8-2\sqrt{15}, find the opposite of each term.
2\sqrt{15}+2\sqrt{15}
Subtract 8 from 8 to get 0.
4\sqrt{15}
Combine 2\sqrt{15} and 2\sqrt{15} to get 4\sqrt{15}.
\left(\sqrt{5}\right)^{2}+2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}-\sqrt{3}\right)^{2}
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\sqrt{5}+\sqrt{3}\right)^{2}.
5+2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}-\sqrt{3}\right)^{2}
The square of \sqrt{5} is 5.
5+2\sqrt{15}+\left(\sqrt{3}\right)^{2}-\left(\sqrt{5}-\sqrt{3}\right)^{2}
To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.
5+2\sqrt{15}+3-\left(\sqrt{5}-\sqrt{3}\right)^{2}
The square of \sqrt{3} is 3.
8+2\sqrt{15}-\left(\sqrt{5}-\sqrt{3}\right)^{2}
Add 5 and 3 to get 8.
8+2\sqrt{15}-\left(\left(\sqrt{5}\right)^{2}-2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{5}-\sqrt{3}\right)^{2}.
8+2\sqrt{15}-\left(5-2\sqrt{5}\sqrt{3}+\left(\sqrt{3}\right)^{2}\right)
The square of \sqrt{5} is 5.
8+2\sqrt{15}-\left(5-2\sqrt{15}+\left(\sqrt{3}\right)^{2}\right)
To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.
8+2\sqrt{15}-\left(5-2\sqrt{15}+3\right)
The square of \sqrt{3} is 3.
8+2\sqrt{15}-\left(8-2\sqrt{15}\right)
Add 5 and 3 to get 8.
8+2\sqrt{15}-8+2\sqrt{15}
To find the opposite of 8-2\sqrt{15}, find the opposite of each term.
2\sqrt{15}+2\sqrt{15}
Subtract 8 from 8 to get 0.
4\sqrt{15}
Combine 2\sqrt{15} and 2\sqrt{15} to get 4\sqrt{15}.