QQuestionMathematics
QuestionMathematics
What is $\sqrt{30}$ in simplified form?
$\bigcirc 5 \sqrt{6}$
$\bigcirc 3 \sqrt{5}$
$\bigcirc 3 \sqrt{10}$
$\bigcirc \sqrt{30}$ can't be simplified.
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Answer
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Step 1:: Identify the prime factors of the number under the square root.
The prime factors of 30 are 2, 3, and 5.
Step 2:: Determine if any pair of prime factors can be used to create a perfect square.
In this case, we can use the prime factor 3 to create a perfect square, as 3^2 = 9.
Step 3:: Divide out the perfect square.
\sqrt{30} = \sqrt{2 \times \bcancel{3} \times 5} = \sqrt{2 \times 5} \times \frac{\bcancel{3}}{\sqrt{3}}
Step 4:: Simplify the remaining square root, if possible.
In this case, $\sqrt{2 \times 5}$ cannot be simplified further, as it does not contain any perfect squares.
Step 5:: Rewrite the simplified expression.
\sqrt{30} = \sqrt{2 \times 5} \times \frac{3}{1} = 3\sqrt{2 \times 5} = 3\sqrt{10}
We can rewrite the simplified expression as follows:
Final Answer
$\sqrt{30}$ can be simplified to $3\sqrt{10}$.
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