You can simplify the term by approximation! Here is the approach:
Let y = √x = x^(½). Then,
dy/dx = ½ * x^(-½) = 1/(2√x)
Select 115² to be x. Then, we obtain:
y = 115
dy/dx = 1/(2 * 115) = 1 / 230
Therefore, we obtain this equation:
y - 115 = 1/230 * (x - 115²)
If x = 13144, then we have:
y - 115 = 1/230 * (13144 - 115²)
y = 1/230 * (13144 - 115²) + 115
≈ 114.65
OR
What you can do is to factor out each term by term and extract the perfect square factor out of the √. For instance:
√(13144) = √(4 * 3286) = 2√3286
25 + 144 = 169√169 = 13
Are you familiar with the concept of the square root of -1?This is represented by iFor the square root of 243 we can get i involved and say wer are looking for the square root ot [256 - 13(i2)]This can be simplified to [+/-16 - √13(i)]
the square root of 122+52 (144 + 25 = 169) which is 13.
The square root of 169 = ± 13
√144 < √165 < √169 12 < √165 < 13
Square root of 25= 5. 5 + 144 + 13 = 162.
The square roots of 13 cannot be simplified.
25 + 144 = 169√169 = 13
It is: 13-144 = -131
It can't be simplified because the square root of 13 is an irrational number that can not be expressed as a fraction
Are you familiar with the concept of the square root of -1?This is represented by iFor the square root of 243 we can get i involved and say wer are looking for the square root ot [256 - 13(i2)]This can be simplified to [+/-16 - √13(i)]
The square root of 144 (12*12) and the square root of 169 (13*13).
If the 13 was the long side (hypoteneuse), the other side would be the square root of 13²-5² = square root of 169-25 = square root of 144 = 12. (according to Pythagoras). If the 13 was a short side, the other is square root of 13² + 5² = square root of 169+25 = square root of 194, or about 13.93
between 12 and 13 (144 and 169)
sqrt(117) = sqrt(9*13) = sqrt(9)*sqrt(13) = 3*sqrt(13)
As 91 = 7 × 13, √91 doesn't really simplify. It can be changed into: √91 = √(7×13) = √7 √13
the square root of 122+52 (144 + 25 = 169) which is 13.