Square Root Of 5684 In Simplest Radical Form
Simplify the square root of 5684 to its lowest radical form.ANSWER: 14√29
14√29 is in the lowest radical form.
Simplified Radical Form of √5684
One of the main facts used to simplify square roots is that the square root of a product is equal to the product of square roots: √(x×y) = √x×√y
Explanation:
When we find square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them.
Step 1: List Factors
To simplify √5684, we need to divide into factors.
√5684 = √2 x √2 x √7 x √7 x √29Step 2: List Perfect Squares
1 is a perfect square and divides 5684
4 is a perfect square and divides 5684
49 is a perfect square and divides 5684
196 is a perfect square and divides 5684
Step 3: Divide To Perfect Square
Divide 5684 by the largest perfect square you found in the previous step:
Step 4: Calculate The Square Root
Calculate the square root of the largest perfect square:
Final Step :
Put Steps 3 and 4 together to get the square root of 5684 in its simplest form: 14√29
How do you simplify √5684
The general approach is to first check if it is a perfect square. If so, you have the answer. If it is not a perfect square, see if any of its factors are perfect squares, or can be combined to make square numbers.
Find the lowest prime number that can divide 5684. Divide 5684 repeatedly using the long division method till you reach 1.
A pair of factor 'twins' under a square root sign (radical) form a single factor outside of it.
Factors that do not have a twin remain under the radical. Multiply them back together and leave them in there.
So, the answer is 14√29.
Simplified Decimal Form of √5684
The square root of 5684 is approximately 75.392 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √59 | Square root of 59 is the simplest radical form. | √59 |
| √35 | Square root of 35 is the simplest radical form. | √5 x √7 |
| √46 | Square root of 46 is the simplest radical form. | √2 x √23 |
| √987 | Square root of 987 is the simplest radical form. | √3 x √7 x √47 |
| √642 | Square root of 642 is the simplest radical form. | √2 x √3 x √107 |
| √254 | Square root of 254 is the simplest radical form. | √2 x √127 |
| √3309 | Square root of 3309 is the simplest radical form. | √3 x √1103 |
| √2658 | Square root of 2658 is the simplest radical form. | √2 x √3 x √443 |
| √3841 | Square root of 3841 is the simplest radical form. | √23 x √167 |