Respuesta :

mathstudent55
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.

[tex] 5 \sqrt{8} - \sqrt{18} -2 \sqrt{2} = [/tex]

[tex]= 5 \sqrt{4 \times 2} - \sqrt{9 \times 2} -2 \sqrt{2} [/tex]

[tex]= 5 \times 2\sqrt{2} - 3 \sqrt{2} -2 \sqrt{2} [/tex]

[tex]= 10\sqrt{2} - 3 \sqrt{2} -2 \sqrt{2} [/tex]

[tex]= 5\sqrt{2} [/tex]
lublana

Answer:

[tex]5\sqrt2[/tex]

Step-by-step explanation:

We are given that an expression

[tex]5\sqrt8-\sqrt{18}-2\sqrt2[/tex]

We have to simplify the given expression.

Factorize each term

[tex]5\sqrt{2\times 2\times 2}-\sqrt{2\times 3\times 3}-2\sqrt2[/tex]

[tex]5\times 2\sqrt2-3\sqrt2-2\sqrt2[/tex]

[tex]10\sqrt2-3\sqrt2-2\sqrt2[/tex]

By simplification

[tex]10\sqrt2-5\sqrt2[/tex]

Taking common[tex]\sqrt2[/tex] form each term

[tex](10-5)\sqrt2[/tex]

[tex]5\sqrt2[/tex]  ( by simplification)

Hence, [tex]5\sqrt8-\sqrt{18}-2\sqrt2=5\sqrt2[/tex]

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