Add or subtract. Assume all variables represent non-negative real numbers.
13√128 + 6√169 - 7√121 - 11√162
13√128 + 6√169 - 7√121 - 11√162
13√(64*2) + 6*13 - 7*11 - 11√(81*2)
13*8√2 + 78 - 77 - 11*9√2
104√2 + 1 - 99√2
1 + 5√2
don't just blindly copy and paste. There are no variables here, so that 2nd sentence is just noise.
Sum = 13*sqrt(64*2) + 6*13 - 7*11 - 11*sqrt(81*2),
Sum = 13*8*sqrt2 + 78 - 77 - 11*9*sqrt2
Sum = 104*sqrt2 + 1 - 99*sqrt2,
Sum = 5*Sqrt2 + 1 = 8.071.
To simplify the given expression, we need to evaluate each square root separately and then perform the addition and subtraction.
First, let's simplify the square roots:
- √128 can be simplified as √(64 * 2), and since 64 is a perfect square (8 * 8 = 64), we can take it out of the square root. So, √128 becomes 8√2.
- √169 is equal to 13, as 13^2 = 169.
- √121 is equal to 11, as 11^2 = 121.
- √162 can be simplified as √(81 * 2), and since 81 is a perfect square (9 * 9 = 81), we can take it out of the square root. So, √162 becomes 9√2.
Now let's substitute these simplified square roots back into the original expression and perform the addition and subtraction:
13√128 + 6√169 - 7√121 - 11√162
= 13 * 8√2 + 6 * 13 - 7 * 11 - 11 * 9√2
= 104√2 + 78 - 77 - 99√2
Now, we can combine like terms. The terms with √2 and the constant terms can be added/subtracted separately:
(104√2 - 99√2) + (78 - 77)
= 5√2 + 1
Therefore, the simplified form of the given expression is 5√2 + 1.