Question

11 sq root 45-4 sq root 5

Answer 1

Answer:

$29\sqrt{5}$

Step-by-step explanation:

We want to simplify:

$11\sqrt{45}-4\sqrt{5}$

We need to simplify the first radical before we can subtract

$11\sqrt{9\times5}-4\sqrt{5}$

$11\sqrt{9} \times\sqrt{5}-4\sqrt{5}$

This implies that:

$11\times 3\times\sqrt{5}-4\sqrt{5}$

$33\sqrt{5}-4\sqrt{5}$

We have now obtained like surds.

We simplify to get:

$29\sqrt{5}$

Answer 2

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