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What is the simplified form of the following expression? 2 StartRoot 27 EndRoot + StartRoot 12 EndRoot minus 3 StartRoot 3 EndRoot minus 2 StartRoot 12 EndRoot StartRoot 3 EndRoot 9 StartRoot 3 EndRoot 11 StartRoot 3 EndRoot 15 StartRoot 3 EndRoot

Sagot :

Given:

The expression is:

[tex]2\sqrt{27}+\sqrt{12}-3\sqrt{3}-2\sqrt{12}[/tex]

To find:

The simplified form of the given expression.

Solution:

We have,

[tex]2\sqrt{27}+\sqrt{12}-3\sqrt{3}-2\sqrt{12}[/tex]

It can be written as:

[tex]=2\sqrt{9\times 3}+\sqrt{4\times 3}-3\sqrt{3}-2\sqrt{4\times 3}[/tex]

[tex]=2(3\sqrt{3})+2\sqrt{3}-3\sqrt{3}-2(2\sqrt{3})[/tex]

[tex]=6\sqrt{3}-\sqrt{3}-4\sqrt{3}[/tex]

[tex]=\sqrt{3}[/tex]

Therefore, the correct option is A.

Lanuel

Based on the calculations, the simplified value of the expression above is equal to: A. √3.

What is an expression?

An expression refers to a mathematical equation which is used to show the relationship between two (2) or more numerical quantities such as being equal.

How to simplify the value of an expression?

In this exercise, we would simplify the given expression by solving the roots and collecting like terms as follows:

2√27 + √12 - 3√3 - 2√12

2(√3 × √9) + (√4 × √3) - 3√3 - 2(√4 × √3)

2(√3) × 3) + (2 × √3) - 3√3 - 2(2 × √3)

6√3 + 2√3 - 3√3 - 4√3

8√3 - 7√3 = √3.

Read more on expressions here: brainly.com/question/13170908

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