Simplify the following expression: $\frac{\sqrt{48}}{\sqrt{6}}$
Understand the Problem
The question requires simplifying a fraction that contains square roots in both numerator and denominator. We will simplify the fraction by dividing the numbers inside the square roots, and then simplifying if possible.
Answer
$2\sqrt{2}$
Answer for screen readers
$2\sqrt{2}$
Steps to Solve
- Combine the square roots
We can combine the square roots in the numerator and the denominator into a single square root:
$\frac{\sqrt{48}}{\sqrt{6}} = \sqrt{\frac{48}{6}}$
- Simplify the fraction inside the square root
Divide 48 by 6:
$\sqrt{\frac{48}{6}} = \sqrt{8}$
- Simplify the square root
Find the prime factorization of 8: $8 = 2 \cdot 2 \cdot 2 = 2^3 = 2^2 \cdot 2$. Then we can simplify $\sqrt{8}$ as follows
$\sqrt{8} = \sqrt{2^2 \cdot 2} = \sqrt{2^2} \cdot \sqrt{2} = 2\sqrt{2}$
$2\sqrt{2}$
More Information
The simplified form of $\frac{\sqrt{48}}{\sqrt{6}}$ is $2\sqrt{2}$. This is an irrational number.
Tips
A common mistake is not simplifying the square root completely after dividing the numbers inside the square roots. For example, stopping at $\sqrt{8}$ would not be considered fully simplified.
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