im stuck on a question and i don't kno wat the answer shud b...
Is the square root of 8 + the square root of 10 the same as the square root of 8+10?
Use a grid and lengths of line segments to give a geometric argument.
thx for ur help ;]
clearly not equal!
√8 is 2 something
√10 is 3 something
so √8+√10 > 5
but √(8+10) or √18 is < 5
thnk u veryyy much
To answer this question, we need to compare the sum of the square roots of 8 and 10 with the square root of their sum.
1. Start by drawing a grid on a piece of paper. This grid will help us visualize the lengths of line segments.
2. Label one side of the grid with the numbers 0, 1, 2, 3, etc., representing the integers.
3. We will use the Pythagorean theorem to calculate the lengths of line segments on the grid. According to the Pythagorean theorem, the length of the hypotenuse of a right triangle equals the square root of the sum of the squares of the other two sides.
4. Draw a right-angled triangle in the grid, with one side of length 8 and the other side of length 10. Calculate the length of the hypotenuse using the Pythagorean theorem:
Length of hypotenuse = sqrt((Length of side 1)^2 + (Length of side 2)^2)
Length of hypotenuse = sqrt(8^2 + 10^2)
Length of hypotenuse = sqrt(64 + 100)
Length of hypotenuse = sqrt(164)
5. Now, draw another right-angled triangle, where one side has length sqrt(8) and the other side has length sqrt(10). Calculate the length of the hypotenuse:
Length of hypotenuse = sqrt((Length of side 1)^2 + (Length of side 2)^2)
Length of hypotenuse = sqrt((sqrt(8))^2 + (sqrt(10))^2)
Length of hypotenuse = sqrt(8 + 10)
Length of hypotenuse = sqrt(18)
6. By comparing the lengths of the two hypotenuses, we can see that sqrt(164) is not the same as sqrt(18).
Therefore, the square root of 8 plus the square root of 10 is NOT the same as the square root of (8 + 10).
Using the grid and lengths of line segments, we have provided a geometric argument to support this conclusion.