Evaluate
10-2\sqrt{21}\approx 0.83484861
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10-2\sqrt{21}
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\left(\sqrt{7}\right)^{2}-2\sqrt{7}\sqrt{3}+\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{7}-\sqrt{3}\right)^{2}.
7-2\sqrt{7}\sqrt{3}+\left(\sqrt{3}\right)^{2}
The square of \sqrt{7} is 7.
7-2\sqrt{21}+\left(\sqrt{3}\right)^{2}
To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.
7-2\sqrt{21}+3
The square of \sqrt{3} is 3.
10-2\sqrt{21}
Add 7 and 3 to get 10.
\left(\sqrt{7}\right)^{2}-2\sqrt{7}\sqrt{3}+\left(\sqrt{3}\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{7}-\sqrt{3}\right)^{2}.
7-2\sqrt{7}\sqrt{3}+\left(\sqrt{3}\right)^{2}
The square of \sqrt{7} is 7.
7-2\sqrt{21}+\left(\sqrt{3}\right)^{2}
To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.
7-2\sqrt{21}+3
The square of \sqrt{3} is 3.
10-2\sqrt{21}
Add 7 and 3 to get 10.
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