Question

simplyfy root3+root2/root3-root2 if root6is 2.45(approx)​

Answer 1

Answer:

Start with a guess, it doesn't have to be that close, so start with 2, whose square is 4. Not too good.

Start with a guess, it doesn't have to be that close, so start with 2, whose square is 4. Not too good.A closer approximation is the mean of 2 and 6/2, which is 2.5. Its square is 6.25, so we're getting closer.

Start with a guess, it doesn't have to be that close, so start with 2, whose square is 4. Not too good.A closer approximation is the mean of 2 and 6/2, which is 2.5. Its square is 6.25, so we're getting closer.Repeat the algorithm. A closer approximation is the mean of 2.5 and 6/2.5 = 2.45. That's the number in the question. It's square is 6.0025, accurate to three significant figures.

Start with a guess, it doesn't have to be that close, so start with 2, whose square is 4. Not too good.A closer approximation is the mean of 2 and 6/2, which is 2.5. Its square is 6.25, so we're getting closer.Repeat the algorithm. A closer approximation is the mean of 2.5 and 6/2.5 = 2.45. That's the number in the question. It's square is 6.0025, accurate to three significant figures.We can go around again and get the mean of 2.45 and 6/2.45 = 2.449489… Its square is 6.00000026… Very close.

Start with a guess, it doesn't have to be that close, so start with 2, whose square is 4. Not too good.A closer approximation is the mean of 2 and 6/2, which is 2.5. Its square is 6.25, so we're getting closer.Repeat the algorithm. A closer approximation is the mean of 2.5 and 6/2.5 = 2.45. That's the number in the question. It's square is 6.0025, accurate to three significant figures.We can go around again and get the mean of 2.45 and 6/2.45 = 2.449489… Its square is 6.00000026… Very close.So we can conclude that 2.45 is equal to the square root of 6 to 2 decimal places / 3 significant figures.