How do you simplify 10 square root 96
The Correct Answer and Explanation is:
To simplify 109610 \sqrt{96}1096, let’s break it down step-by-step.
Step 1: Simplify 96\sqrt{96}96
Start by factoring 96 into its prime factors: 96=25×396 = 2^5 \times 396=25×3
Now, we can break the square root into the square root of the factors: 96=25×3=24×2×3\sqrt{96} = \sqrt{2^5 \times 3} = \sqrt{2^4 \times 2 \times 3}96=25×3=24×2×3
Since 24=22=4\sqrt{2^4} = 2^2 = 424=22=4, we can simplify: 96=46\sqrt{96} = 4\sqrt{6}96=46
Step 2: Multiply by 10
Now, substitute 96\sqrt{96}96 with 464\sqrt{6}46 into the original expression: 1096=10×46=40610\sqrt{96} = 10 \times 4\sqrt{6} = 40\sqrt{6}1096=10×46=406
Final Answer:
Thus, 109610\sqrt{96}1096 simplifies to 40640\sqrt{6}406.
Explanation:
- First, we factor 96 to find the perfect square part (in this case 242^424) and the remaining factor (the 2×32 \times 32×3 part).
- By simplifying 96\sqrt{96}96, we get 464\sqrt{6}46 because 24=4\sqrt{2^4} = 424=4.
- Finally, we multiply the result by 10 to get 40640\sqrt{6}406.
This process makes it easier to work with square roots by removing the unnecessary complexity of large numbers inside the square root, making the expression more manageable.
