Question

What is −2√20 − √125 in simplest radical form?

Answer 1

Solving -5\sqrt{5} we get
`\mathbf{-9√(5)}`

Explanation:

We need to solve
`-2√(20)-√(125)`

Factors of 20 are: 2x2x5

Factors of 125 are: 5x5x5

Replacing 20 and 125 with their factors.

`-2√(20)-√(125)\\=-2√(2*2*5)-√(5*5*5)\\=-2√(2^2*5)-√(5^2*5)\\We \ know \ √(a^2)=a \\=-2√(2^2)√(5)-√(5^2)√(5)\\=-2*2√(5)-5√(5)\\=-4√(5)-5√(5)\\Taking \ √(5) \ common\\=(-4-5)√(5)\\=-9√(5)`

So, solving -5\sqrt{5} we get
`\mathbf{-9√(5)}`