# How do you simplify #5sqrt8-4sqrt72+3sqrt96#?

By signing up, you agree to our Terms of Service and Privacy Policy

To simplify (5\sqrt{8} - 4\sqrt{72} + 3\sqrt{96}), first, factor the numbers under the square roots:

[ 8 = 2 \times 2 \times 2 ] [ 72 = 2 \times 2 \times 2 \times 3 \times 3 ] [ 96 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 ]

Then, simplify each square root:

[ \sqrt{8} = \sqrt{2 \times 2 \times 2} = 2\sqrt{2} ] [ \sqrt{72} = \sqrt{2 \times 2 \times 2 \times 3 \times 3} = 6\sqrt{2} ] [ \sqrt{96} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 3} = 4\sqrt{6} ]

Now, substitute these simplified square roots back into the expression:

[ 5\sqrt{8} - 4\sqrt{72} + 3\sqrt{96} = 5(2\sqrt{2}) - 4(6\sqrt{2}) + 3(4\sqrt{6}) ]

[ = 10\sqrt{2} - 24\sqrt{2} + 12\sqrt{6} ]

[ = (10 - 24)\sqrt{2} + 12\sqrt{6} ]

[ = -14\sqrt{2} + 12\sqrt{6} ]

So, (5\sqrt{8} - 4\sqrt{72} + 3\sqrt{96}) simplifies to (-14\sqrt{2} + 12\sqrt{6}).

By signing up, you agree to our Terms of Service and Privacy Policy

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7