Question

What is the simplified form of the following expression? 5sqrt 8-sqrt18-2sqrt2

Answer 1

5 sqrt2.

Explanation:

sqrt8 = sqrt4 * sqrt2 = 2 sqrt2

sqrt18 = sqrt9 * sqrt2 = 3 sqrt2

So simplifying:

5sqrt 8 - sqrt18 - 2 sqrt2

= 5*2sqrt2 - 3 sqrt 2 - 2 sqrt2

= 10 sqrt2 - 5 sqrt2

= 5 sqrt2 (answer).

Answer 2

For this case we must simplify the following expression:

`5 \sqrt {8} - \sqrt {18} -2 \sqrt {2}`

Rewriting we have:

`8 = 2 * 2 * 2 = 2 ^ 2 * 2\\18 = 9 * 2 = 3 ^ 2 * 2\\5 \sqrt {2 ^ 2 * 2} - \sqrt {3 ^ 2 * 2} -2 \sqrt {2} =`

We have that by definition of properties of roots and powers it is fulfilled:

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

So:

`5 * 2 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -5 \sqrt {2} =\\5 \sqrt {2}`

Answer:

`5 \sqrt {2}`