Question

What is the simplified form of the following expression?

Answer 1

You have sqrt(8), sqrt(18), and sqrt(2).
You need to simplify the radicals.
sqrt(2) is already simplified.
For both sqrt(8) and sqrt(18), you need to factor out the greatest perfect square.

8 = 4 * 2
You can take the square root of 4 and put it outside the root.

18 = 9 * 2
You can take the square root of 9 and put it outside the root.

$5 \sqrt{8} - \sqrt{18} -2 \sqrt{2} =$

$= 5 \sqrt{4 \times 2} - \sqrt{9 \times 2} -2 \sqrt{2}$

$= 5 \times 2\sqrt{2} - 3 \sqrt{2} -2 \sqrt{2}$

$= 10\sqrt{2} - 3 \sqrt{2} -2 \sqrt{2}$

$= 5\sqrt{2}$

Answer 2

Answer:

$5\sqrt2$

Step-by-step explanation:

We are given that an expression

$5\sqrt8-\sqrt{18}-2\sqrt2$

We have to simplify the given expression.

Factorize each term

$5\sqrt{2\times 2\times 2}-\sqrt{2\times 3\times 3}-2\sqrt2$

$5\times 2\sqrt2-3\sqrt2-2\sqrt2$

$10\sqrt2-3\sqrt2-2\sqrt2$

By simplification

$10\sqrt2-5\sqrt2$

Taking common$\sqrt2$ form each term

$(10-5)\sqrt2$

$5\sqrt2$  ( by simplification)

Hence, $5\sqrt8-\sqrt{18}-2\sqrt2=5\sqrt2$