Square Root Of 54700816 In Simplest Radical Form
Simplify the square root of 54700816 to its lowest radical form.ANSWER: 7396√1
7396√1 is in the lowest radical form.
Simplified Radical Form of √54700816
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 √54700816, we need to divide into factors.
√54700816 = √2 x √2 x √2 x √2 x √43 x √43 x √43 x √43Step 2: List Perfect Squares
1 is a perfect square and divides 54700816
4 is a perfect square and divides 54700816
16 is a perfect square and divides 54700816
1849 is a perfect square and divides 54700816
7396 is a perfect square and divides 54700816
29584 is a perfect square and divides 54700816
3418801 is a perfect square and divides 54700816
13675204 is a perfect square and divides 54700816
54700816 is a perfect square and divides 54700816
Step 3: Divide To Perfect Square
Divide 54700816 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 54700816 in its simplest form: 7396√1
How do you simplify √54700816
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 54700816. Divide 54700816 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 7396√1.
Simplified Decimal Form of √54700816
The square root of 54700816 is approximately 7396 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √12 | 2√3 | √2 x √2 x √3 |
| √83 | Square root of 83 is the simplest radical form. | √83 |
| √52 | 2√13 | √2 x √2 x √13 |
| √906 | Square root of 906 is the simplest radical form. | √2 x √3 x √151 |
| √687 | Square root of 687 is the simplest radical form. | √3 x √229 |
| √555 | Square root of 555 is the simplest radical form. | √3 x √5 x √37 |
| √1230 | Square root of 1230 is the simplest radical form. | √2 x √3 x √5 x √41 |
| √2017 | Square root of 2017 is the simplest radical form. | √2017 |
| √8218 | Square root of 8218 is the simplest radical form. | √2 x √7 x √587 |