Find the square root of 45
The square root of 45 is approximately 6.7082
To find the square root of 45, you can use either a calculator, mathematical formula, or an estimation method. Let's go through each method step by step:
1. Using a calculator:
Most calculators have a built-in square root function. To find the square root of 45, you would input "45" into the calculator and then press the square root (√) button. The calculator will give you the exact decimal value of the square root of 45.
2. Mathematical formula:
If you prefer to do the calculation by hand, the square root of 45 can be found using the formula √x = x^(1/2). In this case, x equals 45. You can raise 45 to the power of 1/2, which can be written as 45^(1/2). Evaluating this expression will give you the square root of 45.
3. Estimation method:
If you don't require an exact value and just need an approximate answer, you can use an estimation method. First, identify the closest perfect square to 45, which is 49 (√49 = 7). Then, consider that 45 is smaller than 49 but larger than 36 (√36 = 6). Now, you can estimate that the square root of 45 is somewhere between 6 and 7. You can refine this estimate by making smaller increments until you get a desired level of accuracy.
Using any of these methods, you can find the square root of 45.
45 = 9*5
So √45 = 3√5
That is correct! Since 45 can be expressed as the product of 9 and 5, its square root can be simplified further as 3√5.
To find the square root of 45, follow these steps:
Step 1: Start by estimating the square root. In this case, a reasonable estimate is √45 ≈ 6.
Step 2: Take the estimate (6) and square it. 6^2 = 36.
Step 3: Subtract the result from the original number: 45 - 36 = 9.
Step 4: Double the original estimate (6) and append an unknown variable, let's call it 'x', to represent the decimal part of the square root. So, 2 * 6 = 12x.
Step 5: Multiply 'x' with the unknown variable 'x' and express it as an equation: x^2 = 9.
Step 6: Solve the equation for 'x'. Taking the square root of both sides, you get: x = √9.
Step 7: Simplify the square root of 9, which is 3.
Step 8: The square root of 45 can be expressed as: √45 ≈ 6 + 3 = 9.
Therefore, the approximate square root of 45 is 9.