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If you have 8 twenty-dollar bills and spend 3 twenty-dollar bills, you have 5 twenty-dollar bills left. You wouldn't subtract the twenties themselves and say you have 5 zero-dollar bills — and subtracting radicals follows the exact same logic.
In any radical expression like 858\sqrt{5}, the radicand is the value resting inside the radical sign, while the coefficient is the number multiplied out in front.
Why do like radicands stay untouched during subtraction? Because of the distributive property in reverse: factoring out the common radical leaves ax−bx=(a−b)xa\sqrt{x} - b\sqrt{x} = (a - b)\sqrt{x}.
So what does this look like when we put it into action with concrete numbers?

Subtracting with Whole Number Coefficients

Consider the expression 97−479\sqrt{7} - 4\sqrt{7}. Since both terms share the exact same radicand of 77, you subtract only the coefficients: (9−4)7=57(9 - 4)\sqrt{7} = 5\sqrt{7}.
That feels straightforward when both numbers are clearly visible out front. But what happens when a radical stands completely on its own?

The Invisible Coefficient

Just as the algebraic term xx represents 1x1x, a lone radical like 3\sqrt{3} has an unwritten coefficient of 11.
When simplifying 73−37\sqrt{3} - \sqrt{3}, rewrite the second term as 131\sqrt{3}. Subtracting gives (7−1)3=63(7 - 1)\sqrt{3} = 6\sqrt{3}, rather than mistakenly dropping the radical or guessing 77.
What if an expression strings together more than two terms, or the subtraction drives your total below zero?