Square Root Of 331776 In Simplest Radical Form
Simplify the square root of 331776 to its lowest radical form.ANSWER: 576√1
576√1 is in the lowest radical form.
Simplified Radical Form of √331776
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 √331776, we need to divide into factors.
√331776 = √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 √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 331776
4 is a perfect square and divides 331776
9 is a perfect square and divides 331776
16 is a perfect square and divides 331776
36 is a perfect square and divides 331776
64 is a perfect square and divides 331776
81 is a perfect square and divides 331776
144 is a perfect square and divides 331776
256 is a perfect square and divides 331776
324 is a perfect square and divides 331776
576 is a perfect square and divides 331776
1024 is a perfect square and divides 331776
1296 is a perfect square and divides 331776
2304 is a perfect square and divides 331776
4096 is a perfect square and divides 331776
5184 is a perfect square and divides 331776
9216 is a perfect square and divides 331776
20736 is a perfect square and divides 331776
36864 is a perfect square and divides 331776
82944 is a perfect square and divides 331776
331776 is a perfect square and divides 331776
Step 3: Divide To Perfect Square
Divide 331776 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 331776 in its simplest form: 576√1
How do you simplify √331776
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 331776. Divide 331776 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 576√1.
Simplified Decimal Form of √331776
The square root of 331776 is approximately 576 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √90 | 3√10 | √2 x √3 x √3 x √5 |
| √75 | 5√3 | √3 x √5 x √5 |
| √32 | 4√2 | √2 x √2 x √2 x √2 x √2 |
| √757 | Square root of 757 is the simplest radical form. | √757 |
| √158 | Square root of 158 is the simplest radical form. | √2 x √79 |
| √174 | Square root of 174 is the simplest radical form. | √2 x √3 x √29 |
| √5406 | Square root of 5406 is the simplest radical form. | √2 x √3 x √17 x √53 |
| √1638 | 3√182 | √2 x √3 x √3 x √7 x √13 |
| √7959 | Square root of 7959 is the simplest radical form. | √3 x √7 x √379 |