It is about 9.487 rounded to 3 decimal places
Not "number", but "numbers" - there are infinitely many. For a start, get a decimal approximation (on your calculator) for the square root of 2 and 3, then get some terminating decimals that are between those.
1) The best method is usually to use a calculator that has the square root function (i.e., just about any calculator), since the other methods are quite cumbersome. 2) You can try squaring different numbers. If you want the square root of 2, 1.4 squared is 1.96, while 1.5 squared is 2.25, so the actual square root must be somewhere between 1.4 and 1.5. Continue experimenting with 1.45, 1.42, etc. 3) If you have an approximation to a square root, you can get a better approximation as follows. As an example, let's say that your approximation for the square root of 2 is 1.4. Now, divide 2 / 1.4. The answer is approximately 1.428. Since this means that 1.4 x 1.428 = 2, the actual square root of 2 must be somewhere between 1.4 and 1.428. Taking the average of both, in this case 1.414, gives you a better approximation. Repeat, until you have the desired precision. This method is much faster than method (2); with every cycle, the amount of correct significant digits should be approximately twice the amount of the previous approximation.
10 square root of 3.
3(3 square root of 2) = 9(square root of 2)
It is about 9.487 rounded to 3 decimal places
In radical form, 3* sqrt(41). The decimal approximation is 19.20937271.
It is somewhere between 3 and 4. You can get a better approximation by using your calculator to get the square root of 11.
You can get a decimal approximation with a calculator, with Excel, etc. But if you want to keep it as a square root, the "standard form" is considered to be one that has no square roots in the denominator. In this case, to get rid of the square root in the denominator, you multiply both numerator and denominator by the square root of 5, with the following result: 3 / root(5) = 3 root(5) / root(5) x root(5) = 3 root(5) / 5 That is, three times the square root of 5, divided by 5.
Not "number", but "numbers" - there are infinitely many. For a start, get a decimal approximation (on your calculator) for the square root of 2 and 3, then get some terminating decimals that are between those.
1) The best method is usually to use a calculator that has the square root function (i.e., just about any calculator), since the other methods are quite cumbersome. 2) You can try squaring different numbers. If you want the square root of 2, 1.4 squared is 1.96, while 1.5 squared is 2.25, so the actual square root must be somewhere between 1.4 and 1.5. Continue experimenting with 1.45, 1.42, etc. 3) If you have an approximation to a square root, you can get a better approximation as follows. As an example, let's say that your approximation for the square root of 2 is 1.4. Now, divide 2 / 1.4. The answer is approximately 1.428. Since this means that 1.4 x 1.428 = 2, the actual square root of 2 must be somewhere between 1.4 and 1.428. Taking the average of both, in this case 1.414, gives you a better approximation. Repeat, until you have the desired precision. This method is much faster than method (2); with every cycle, the amount of correct significant digits should be approximately twice the amount of the previous approximation.
The required distance is the hypotenuse of a right triangle with sides of lengths [2 - (-1)] and [4 - (-3)] = 3 and 7 respectively. From the Pythagorean theorem, this distance is the square root of the sum of the squares of the lengths of each side, in this instance the square root of (9 + 49) or the square root of 58. There is no integral square root, but the decimal approximation is about 7.616 units.
square root 2 times square root 3 times square root 8
Square root (75) / square root (3) = 5
Square root of 6
10 square root of 3.
I believe you are referring to the technique of estimating a square root by division. Step one: Find the nearest perfect square. 16 in this case. step 2: Divide the number (15.625) by 4 (the square root of 16). The result is about 3.906 Step 3: Take the average of 4 and 3.906, which is 3.953. This is an approximation of the square root of 15.625.