How do you simplify 5sqrt7-4sqrt7?

1 Answer

Hello you can simplify this by recognizing that '4' and '5' are coefficients of the radical sqrt7

Explanation:

In this it asks 5sqrt7 - 4sqrt7
Do it by simply subtracting 5-4 = 1
now it is sqrt7 or 'one of sqrt7' since it is like adding and subtracting like terms but similar with radicals.

To make this more clear, we can view the coefficients in front of the radical as entities on their own or write them this way as they are notated by a coefficient;

sqrt7 * sqrt7 * sqrt7 * sqrt7 * sqrt7 - sqrt7 * sqrt7 * sqrt7 * sqrt7

Simply by subtracting 4 from 5, we can get an answer on how many radicals are left in the remainder as notated by 5sqrt7 - 4sqrt7 .

Thus, 5sqrt7 - 4sqrt7=sqrt7

For general examples;
asqrtc - bsqrtc = (a-b)sqrtc