QQuestionMathematics
QuestionMathematics
What is the simplified form of the following expression? 5√8 - √18 - 2√2
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Answer
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Step 1:: Simplify the radicals in the expression.
\sqrt{18} = \sqrt{3^2 imes 2} = 3\sqrt{2}
The radicand of a square root can be simplified if it is a perfect square. In this case, 8 and 18 are not perfect squares, but we can factor them into products of perfect squares: So, the simplified radical forms are:
Step 2:: Substitute the simplified radical forms into the original expression.
5\sqrt{8} - \sqrt{18} - 2\sqrt{2} = 5(2\sqrt{2}) - (3\sqrt{2}) - 2\sqrt{2}
Step 3:: Distribute the 5 and combine like terms.
= 5\sqrt{2}
Final Answer
The simplified form of the expression is 5\sqrt{2}.
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