Question

How to subtract a radical from a whole number?

Answer 1

Although a radical cannot be expressed as a terminating or recurring decimal or a fraction, it can be approximated. This approximation can be expressed as a decimal or a fraction. So if a decimal, ordinary rules of arithmetic apply.
If a fraction, ordinary rules for subtracting fractions apply.
EXAMPLE
99/70 is a good approximation for √2. Let’s see how we would calculate 5-√2=5-99/70=(350-99)/70=251/70=3⁴¹⁄₇₀.
√2=1.4142 to 4 places of decimals. So 5-√2=5-1.4142=3.5858. When we work out 3⁴¹⁄₇₀ as a decimal to 4 places we get 3.5857.
So treat radicals like other real numbers. When giving an answer you may need to say what accuracy you are using (so many decimal places) or the question may tell you how many decimal places are needed.