Square Root Of 2304 In Simplest Radical Form
Simplify the square root of 2304 to its lowest radical form.ANSWER: 48√1
48√1 is in the lowest radical form.
Simplified Radical Form of √2304
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 √2304, we need to divide into factors.
√2304 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 2304
4 is a perfect square and divides 2304
9 is a perfect square and divides 2304
16 is a perfect square and divides 2304
36 is a perfect square and divides 2304
64 is a perfect square and divides 2304
144 is a perfect square and divides 2304
256 is a perfect square and divides 2304
576 is a perfect square and divides 2304
2304 is a perfect square and divides 2304
Step 3: Divide To Perfect Square
Divide 2304 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 2304 in its simplest form: 48√1
How do you simplify √2304
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 2304. Divide 2304 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 48√1.
Simplified Decimal Form of √2304
The square root of 2304 is approximately 48 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √20 | 2√5 | √2 x √2 x √5 |
| √7 | Square root of 7 is the simplest radical form. | √7 |
| √10 | Square root of 10 is the simplest radical form. | √2 x √5 |
| √658 | Square root of 658 is the simplest radical form. | √2 x √7 x √47 |
| √545 | Square root of 545 is the simplest radical form. | √5 x √109 |
| √787 | Square root of 787 is the simplest radical form. | √787 |
| √3704 | 2√926 | √2 x √2 x √2 x √463 |
| √9097 | Square root of 9097 is the simplest radical form. | √11 x √827 |
| √9039 | Square root of 9039 is the simplest radical form. | √3 x √23 x √131 |