- Math: 1 / √2
Description: This is the original expression. We want to find the value of 1 divided by the square root of 2. - Math: (1 / √2) × (√2 / √2)
Description: To rationalize the denominator, we multiply both the numerator and the denominator by √2. - Math: (1 × √2) / 2
Description: After multiplication, the numerator becomes 1 × √2 and the denominator becomes √2 × √2, which simplifies to 2. - Math: √2 / 2
Description: The expression simplifies to √2 / 2.
- Math: 3 / √5
Description: This is the original expression. We want to find the value of 3 divided by the square root of 5. - Math: (3 / √5) × (√5 / √5)
Description: To rationalize the denominator, we multiply both the numerator and the denominator by √5.
2.1 Math: (√5 × √5)
Description: We focus on the denominator, which is √5 × √5. This is the multiplication of the square root of 5 with itself.
2.2 Math: √(5 × 5)
Description: The multiplication inside the square root can be represented as √(5 × 5).
2.3 Math: √25
Description: The multiplication inside the square root simplifies to √25.
2.4 Math: 5
Description: The square root of 25 is 5, so the denominator becomes 5.
- Math: (3 × √5) / 5
Description: After multiplication, the numerator becomes 3 × √5 and the denominator, as we calculated, becomes 5. - Math: 3√5 / 5
Description: The expression simplifies to 3√5 / 5.