Question

What is 10√45 - 7√12 + 2√500 in simplest radical form? You must show all steps for full credit.

Answer 1

`\sf 50√(5)-14√(3)`

Explanation:

Prime factorize 45, 12 and 500 and write the radicals in the simplest form.

`\sf 10√(45)=10√(3*3*5) = 10*3*√(5) = 30√(5)\\\\7√(12)=7√(2*2*3)=7*2√(3) = 14√(3)\\\\2√(500)=2√(2*2*5*5*5)=2*2*5*√(5)=20√(5)`

`\sf 10√(45)-7√(12)+2√(500)=30√(5)-14√(3)+20√(5)\\\\`

`\bf Here, 30√(5) \ and \ 20√(5) \ are \ like \ terms. Combine \ like \ terms.`

`\sf = 30√(5)+20√(5)-14√(3)\\\\=(30+20)√(5)-14√(3)\\\\=50√(5)-14√(3)`