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
The square root of 144 is 12, as 12 multiplied by 12 equals 144. The square root of 25 is 5, as 5 multiplied by 5 equals 25. Therefore, the sum of the square root of 144 and the square root of 25 is 12 + 5, which equals 17.
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)]
To simplify the square root of 91x, you need to factor out any perfect squares from the radicand. In this case, 91 is not a perfect square, but it can be factored into 7 and 13, both of which are prime numbers. Therefore, the square root of 91x cannot be simplified further and remains as sqrt(91x).
the square root of 122+52 (144 + 25 = 169) which is 13.
The square root of 169 = ± 13
Square root of 25= 5. 5 + 144 + 13 = 162.
The square roots of 13 cannot be simplified.
The square root of 144 is 12, as 12 multiplied by 12 equals 144. The square root of 25 is 5, as 5 multiplied by 5 equals 25. Therefore, the sum of the square root of 144 and the square root of 25 is 12 + 5, which equals 17.
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
To simplify the square root of 91x, you need to factor out any perfect squares from the radicand. In this case, 91 is not a perfect square, but it can be factored into 7 and 13, both of which are prime numbers. Therefore, the square root of 91x cannot be simplified further and remains as sqrt(91x).
between 12 and 13 (144 and 169)
sqrt(117) = sqrt(9*13) = sqrt(9)*sqrt(13) = 3*sqrt(13)
the square root of 122+52 (144 + 25 = 169) which is 13.