Square Root Of 884736 In Simplest Radical Form
Simplify the square root of 884736 to its lowest radical form.ANSWER: 384√6
384√6 is in the lowest radical form.
Simplified Radical Form of √884736
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 √884736, we need to divide into factors.
√884736 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 884736
4 is a perfect square and divides 884736
9 is a perfect square and divides 884736
16 is a perfect square and divides 884736
36 is a perfect square and divides 884736
64 is a perfect square and divides 884736
144 is a perfect square and divides 884736
256 is a perfect square and divides 884736
576 is a perfect square and divides 884736
1024 is a perfect square and divides 884736
2304 is a perfect square and divides 884736
4096 is a perfect square and divides 884736
9216 is a perfect square and divides 884736
16384 is a perfect square and divides 884736
36864 is a perfect square and divides 884736
147456 is a perfect square and divides 884736
Step 3: Divide To Perfect Square
Divide 884736 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 884736 in its simplest form: 384√6
How do you simplify √884736
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 884736. Divide 884736 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 384√6.
Simplified Decimal Form of √884736
The square root of 884736 is approximately 940.604 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √5 | Square root of 5 is the simplest radical form. | √5 |
| √48 | 4√3 | √2 x √2 x √2 x √2 x √3 |
| √14 | Square root of 14 is the simplest radical form. | √2 x √7 |
| √591 | Square root of 591 is the simplest radical form. | √3 x √197 |
| √932 | 2√233 | √2 x √2 x √233 |
| √735 | 7√15 | √3 x √5 x √7 x √7 |
| √3110 | Square root of 3110 is the simplest radical form. | √2 x √5 x √311 |
| √3162 | Square root of 3162 is the simplest radical form. | √2 x √3 x √17 x √31 |
| √2788 | 2√697 | √2 x √2 x √17 x √41 |