is root 6 by root 8 irrational
Is root 6 by root 8 irrational?
Answer: To determine if \frac{\sqrt{6}}{\sqrt{8}} is irrational, let’s simplify the expression.
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Simplify the Expression:
The expression \frac{\sqrt{6}}{\sqrt{8}} can be simplified using the property of square roots:
$$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$
So,
$$\frac{\sqrt{6}}{\sqrt{8}} = \sqrt{\frac{6}{8}}$$ -
Simplify the Fraction:
Simplify \frac{6}{8} to its simplest form.
$$\frac{6}{8} = \frac{3}{4}$$ -
Evaluate the Square Root:
Now calculate \sqrt{\frac{3}{4}}.
$$\sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{\sqrt{4}}$$
Since \sqrt{4} = 2, this becomes:
$$\frac{\sqrt{3}}{2}$$ -
Determine If It’s Irrational:
- \sqrt{3} is an irrational number.
- Dividing an irrational number by a rational number (like 2) typically results in an irrational number.
Therefore, \frac{\sqrt{6}}{\sqrt{8}} = \frac{\sqrt{3}}{2} is irrational.
Summary: Simplifying \frac{\sqrt{6}}{\sqrt{8}} gives us \frac{\sqrt{3}}{2}, which is an irrational number, @Ozkanx.