Question

Need help solving this radical question

Answer 1

To simplify
`\((√(5))/(4√(8))\),` rewrite
`\(√(8)\) as \(2√(2)\)`. Rationalize the denominator by multiplying by
`\(√(2)\)`. The simplified form is
`\((√(10))/(16)\)`.

To simplify
`\((√(5))/(4√(8))\)`, we begin by expressing
`\(√(8)\)` as
`\(√(4 * 2)\)`, which is
`\(2√(2)\)`. Substituting this back into the expression yields
`\((√(5))/(4 * 2√(2))\)`. Simplifying the denominator, we get
`\((√(5))/(8√(2))\)`.

To rationalize the denominator, we multiply both the numerator and denominator by
`\(√(2)\)`. This results in
`\((√(5) * √(2))/(8 * √(2) * √(2))\)`. Further simplifying gives
`\((√(10))/(16)\)`. Therefore,
`\((√(5))/(4√(8))\)` simplifies to
`\((√(10))/(16)\)`.

This simplified expression represents the original fraction in a form with no square roots in the denominator, providing a clearer and more manageable representation of the mathematical relationship.