Question

Please help im having so much trouble with this problem: Simplify square root of five times the quantity six minus four square root of three.

9
thirty square root of three
six square root of five minus four square root of fifteen
square root of thirty minus twenty square root of three

Answer 1

Answer: six square root of five minus four square root of fifteen

In symbolic form the answer looks like
`\boldsymbol{6√(5) -4 √(15)}`

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Work Shown:

`√(5)\left(6 - 4√(3)\right)\\\\√(5)\left(6\right) + √(5)\left(-4√(3)\right)\\\\6√(5) -4 √(5*3)\\\\6√(5) -4 √(15)\\\\`

The basic idea is to distribute the outer term
`√(5)` to each term inside. From there you simplify.

For the second to last step, I used the rule that
`√(A)*√(B) = √(A*B)`