Square Root Of 9104 In Simplest Radical Form
Simplify the square root of 9104 to its lowest radical form.ANSWER: 4√569
4√569 is in the lowest radical form.
Simplified Radical Form of √9104
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 √9104, we need to divide into factors.
√9104 = √2 x √2 x √2 x √2 x √569Step 2: List Perfect Squares
1 is a perfect square and divides 9104
4 is a perfect square and divides 9104
16 is a perfect square and divides 9104
Step 3: Divide To Perfect Square
Divide 9104 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 9104 in its simplest form: 4√569
How do you simplify √9104
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 9104. Divide 9104 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 4√569.
Simplified Decimal Form of √9104
The square root of 9104 is approximately 95.415 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √38 | Square root of 38 is the simplest radical form. | √2 x √19 |
| √49 | 7√1 | √7 x √7 |
| √62 | Square root of 62 is the simplest radical form. | √2 x √31 |
| √735 | 7√15 | √3 x √5 x √7 x √7 |
| √402 | Square root of 402 is the simplest radical form. | √2 x √3 x √67 |
| √481 | Square root of 481 is the simplest radical form. | √13 x √37 |
| √9177 | Square root of 9177 is the simplest radical form. | √3 x √7 x √19 x √23 |
| √8474 | Square root of 8474 is the simplest radical form. | √2 x √19 x √223 |
| √8979 | Square root of 8979 is the simplest radical form. | √3 x √41 x √73 |