Square Root Of 104976 In Simplest Radical Form
Simplify the square root of 104976 to its lowest radical form.ANSWER: 324√1
324√1 is in the lowest radical form.
Simplified Radical Form of √104976
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 √104976, we need to divide into factors.
√104976 = √2 x √2 x √2 x √2 x √3 x √3 x √3 x √3 x √3 x √3 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 104976
4 is a perfect square and divides 104976
9 is a perfect square and divides 104976
16 is a perfect square and divides 104976
36 is a perfect square and divides 104976
81 is a perfect square and divides 104976
144 is a perfect square and divides 104976
324 is a perfect square and divides 104976
729 is a perfect square and divides 104976
1296 is a perfect square and divides 104976
2916 is a perfect square and divides 104976
6561 is a perfect square and divides 104976
11664 is a perfect square and divides 104976
26244 is a perfect square and divides 104976
104976 is a perfect square and divides 104976
Step 3: Divide To Perfect Square
Divide 104976 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 104976 in its simplest form: 324√1
How do you simplify √104976
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 104976. Divide 104976 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 324√1.
Simplified Decimal Form of √104976
The square root of 104976 is approximately 324 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √92 | 2√23 | √2 x √2 x √23 |
| √10 | Square root of 10 is the simplest radical form. | √2 x √5 |
| √20 | 2√5 | √2 x √2 x √5 |
| √399 | Square root of 399 is the simplest radical form. | √3 x √7 x √19 |
| √123 | Square root of 123 is the simplest radical form. | √3 x √41 |
| √157 | Square root of 157 is the simplest radical form. | √157 |
| √8497 | Square root of 8497 is the simplest radical form. | √29 x √293 |
| √1218 | Square root of 1218 is the simplest radical form. | √2 x √3 x √7 x √29 |
| √5571 | 3√619 | √3 x √3 x √619 |