Is root 6 by root 8 irrational

General
1

is root 6 by root 8 irrational

2

Is root 6 by root 8 irrational?

Answer: To determine if \frac{\sqrt{6}}{\sqrt{8}} is irrational, let’s simplify the expression.

  1. 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,
    $$\frac{\sqrt{6}}{\sqrt{8}} = \sqrt{\frac{6}{8}}$$

  2. Simplify the Fraction:
    Simplify \frac{6}{8} to its simplest form.
    $$\frac{6}{8} = \frac{3}{4}$$

  3. 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:
    $$\frac{\sqrt{3}}{2}$$

  4. 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.