Question

Simplify. 5√ 10
1) 2√ 2) 2√2 3) 10√2 4) 5√

Answer 1

For this case we have that the expression in its exact form is the same, that is:

`5 \sqrt {10}`

If it is expressed in decimal form we have:

`5 \sqrt {10} = 1.5849`

If we want equivalent expressions, we must first mention the following property of powers and roots:

`\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}`

Then, we can rewrite the expression as:

`5 \sqrt {10} = \sqrt {5 ^ 2 * 10} = \sqrt {25 * 10} = \sqrt {250}`

Answer:

`5 \sqrt {10} = \sqrt {250} = 1.5849`