Question

11 sq root 45-4 sq root 5

Answer 1

First evaluate the sq root of 45.
To do so, you have to find perfect square factors (2 x 2, 3 x 3, 4 x 4, and etc.)

The factors of 45 are 3 x 3 x 5.

Notice that there is a 3 x 3. That means you can get the 3 out of the square root and multiply with the number outside of the square root.

11(3)square root 5 - 4 square root 5

33 square root 5 - 4 square root 5

Subtracting and Adding square roots is the same thing as subtracting and Adding variables. If they have the same variable you can +/-. So if they have the same square root, then can +/-.

Answer: 29 square root 5

Answer 2

`29√(5)`

Explanation:

We want to simplify:

`11√(45)-4√(5)`

We need to simplify the first radical before we can subtract

`11√(9*5)-4√(5)`

`11√(9) *√(5)-4√(5)`

This implies that:

`11* 3*√(5)-4√(5)`

`33√(5)-4√(5)`

We have now obtained like surds.

We simplify to get:

`29√(5)`