Square Root Of 2448 In Simplest Radical Form
Simplify the square root of 2448 to its lowest radical form.ANSWER: 12√17
12√17 is in the lowest radical form.
Simplified Radical Form of √2448
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 √2448, we need to divide into factors.
√2448 = √2 x √2 x √2 x √2 x √3 x √3 x √17Step 2: List Perfect Squares
1 is a perfect square and divides 2448
4 is a perfect square and divides 2448
9 is a perfect square and divides 2448
16 is a perfect square and divides 2448
36 is a perfect square and divides 2448
144 is a perfect square and divides 2448
Step 3: Divide To Perfect Square
Divide 2448 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 2448 in its simplest form: 12√17
How do you simplify √2448
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 2448. Divide 2448 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 12√17.
Simplified Decimal Form of √2448
The square root of 2448 is approximately 49.477 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √23 | Square root of 23 is the simplest radical form. | √23 |
| √85 | Square root of 85 is the simplest radical form. | √5 x √17 |
| √21 | Square root of 21 is the simplest radical form. | √3 x √7 |
| √917 | Square root of 917 is the simplest radical form. | √7 x √131 |
| √299 | Square root of 299 is the simplest radical form. | √13 x √23 |
| √552 | 2√138 | √2 x √2 x √2 x √3 x √23 |
| √9710 | Square root of 9710 is the simplest radical form. | √2 x √5 x √971 |
| √9023 | Square root of 9023 is the simplest radical form. | √7 x √1289 |
| √6429 | Square root of 6429 is the simplest radical form. | √3 x √2143 |