Question

Combine the radicals 5sqrt27-17sqrt3

Answer 1

-2 sqrt3.

Explanation:

sqrt27 = sqrt9 * sqrt3

= 3 sqrt3 So:

5sqrt27 - 17sqrt3

= 5*3 sqrt3 - 17 sqrt 3

= 15 sqrt 3 - 17 sqrt 3

= -2 sqrt3.

Answer 2

For this case we must simplify the following expression:

`5 \sqrt {27} -17 \sqrt {3}`

We have to:

`27 = 3 * 3 * 3 = 3 ^ 2 * 3`

Substituting in the expression we have:

`5 \sqrt {3 ^ 2 * 3} -17 \sqrt {3}`

For properties of powers and roots we have:

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

So:

`5 * 3 \sqrt {3} -17 \sqrt {3} =\\15 \sqrt {3} -17 \sqrt {3} =`

We subtract taking into account that different signs are subtracted and the sign of the major is placed:

`-2 \sqrt {3}`

Answer:

`-2 \sqrt {3}`