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How do you subtract $\sqrt{18}$ from $\sqrt{50}$?

To subtract 18\sqrt{18} from 50\sqrt{50}, we will first evaluate each square root and then perform the subtraction by taking the difference between the larger and the smaller value.

First, let’s simplify the square roots. The square root of 1818 can be expressed in a simpler form:

18=9×2=9×2=32.\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}.

Next, we simplify the square root of 5050:

50=25×2=25×2=52.\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}.

Now we have the following simplified forms:

50=52,\sqrt{50} = 5\sqrt{2}, 18=32.\sqrt{18} = 3\sqrt{2}.

To perform the subtraction, we subtract the coefficients of 2\sqrt{2}:

5232=(53)2=22.5\sqrt{2} - 3\sqrt{2} = (5 - 3)\sqrt{2} = 2\sqrt{2}.

Therefore, the result of subtracting 18\sqrt{18} from 50\sqrt{50} is 222\sqrt{2}.

If you prefer to use decimal approximations for the square roots, you can calculate them directly:

507.071,\sqrt{50} \approx 7.071, 184.243.\sqrt{18} \approx 4.243.

Then, subtracting these approximations gives:

7.0714.2432.828.7.071 - 4.243 \approx 2.828.

Both methods yield consistent results, but simplifying the square roots first often makes the calculations clearer and more precise.

Answered by: Dr. Sarah Wilson
GCSE Physics Tutor
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