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To be as accurate as possible, we have to leave the operation as is. It is not possible to simplify it further.
It is possible to transform irrational numbers into decimals and add them together. However, we will have to use rounding, which will make the answer less precise.
|\sqrt{5}+\sqrt{3}|
|\sqrt{5}+\sqrt{3}\approx2.2361+1.7321\approx3.9682|
The radicands can be grouped for an exact answer or transformed into decimal numbers.
|\sqrt{3}+\sqrt{3}=2\sqrt{3}|
or
|\sqrt{3}+\sqrt{3}\approx1.7321+1.7321\approx3.4642|
Whether it is a fraction consisting of the number pi or a radical accompanied by another term, it is necessary to put everything in decimals and then proceed to the addition.
|\sqrt{2}+\pi\approx1.4142+3.1416\approx4.5558|
When subtracting, we use the same principles as with adding.
|\sqrt{5}-\sqrt{3}\approx2.2361-1.7321\approx0.5040|
|2\sqrt{3}-\sqrt{3}=\sqrt{3}|
or
|2\sqrt{3}-\sqrt{3}\approx3.4641-1.7321\approx1.7321|
|\pi-\sqrt{2}\approx3.1416-1.4142\approx1.7274|
When multiplying a square root with an identical one, the answer is the value of the radicand.
|\sqrt{3}\cdot\sqrt{3}=3|
If the radicals are different, it suffices to recreate an expression where the two radicands multiply together under the same root.
|\sqrt{5}\cdot\sqrt{3}=\sqrt{15}|
When the radical is the same in the numerator and in the denominator, it suffices to reduce them together.
|\frac{\sqrt{2}}{\sqrt{2}}=1|
|\frac{4\sqrt{3}}{2\sqrt{3}}=2|
If the radicals are different, it suffices to create a new fractional expression where the two radicands are found under the same root.
|\frac{\sqrt{12}}{\sqrt{3}}=\sqrt{\frac{12}{3}}=\sqrt{4}=2|
|\frac{2\sqrt{6}}{\sqrt{2}}=2\sqrt{\frac{6}{2}}=2\sqrt{3}|