Answer :
The equivalent to the given expression is √6 + 3√3.
Option A is the correct answer.
What is an expression?
An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
We can simplify the given expression by combining like terms under the radicals:
√6 + 2√3 + √27 - √12
= √(23) + 2√3 + √(3³) - √(2²3)
= √2√3 + 2√3 + 3√3 - 2√3
= √2√3 + 3√3
= √(23) + 3√3
= √6 + 3√3
Therefore,
The equivalent to the given expression is √6 + 3√3.
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Answer:
A
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplifying
[tex]\sqrt{27}[/tex] = [tex]\sqrt{9(3)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{3}[/tex] = 3[tex]\sqrt{3}[/tex]
[tex]\sqrt{12}[/tex] = [tex]\sqrt{4(3)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{3}[/tex] = 2[tex]\sqrt{3}[/tex]
Thus
[tex]\sqrt{6}[/tex] + 2[tex]\sqrt{3}[/tex] + [tex]\sqrt{27}[/tex] - [tex]\sqrt{12}[/tex]
= [tex]\sqrt{6}[/tex] + 2[tex]\sqrt{3}[/tex] + 3[tex]\sqrt{3}[/tex] - 2[tex]\sqrt{3}[/tex] ← collect like terms
= 3[tex]\sqrt{3}[/tex] + [tex]\sqrt{6}[/tex] → A