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 $\boldsymbol{6\sqrt{5} -4 \sqrt{15}}$

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Work Shown:

$\sqrt{5}\left(6 - 4\sqrt{3}\right)\\\\\sqrt{5}\left(6\right) + \sqrt{5}\left(-4\sqrt{3}\right)\\\\6\sqrt{5} -4 \sqrt{5*3}\\\\6\sqrt{5} -4 \sqrt{15}$

The basic idea is to distribute the outer term $\sqrt{5}$ to each term inside. From there you simplify.

For the second to last step, I used the rule that $\sqrt{A}*\sqrt{B} = \sqrt{A*B}$