Square Root Of 373248 In Simplest Radical Form
Simplify the square root of 373248 to its lowest radical form.ANSWER: 432√2
432√2 is in the lowest radical form.
Simplified Radical Form of √373248
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 √373248, we need to divide into factors.
√373248 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3 x √3 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 373248
4 is a perfect square and divides 373248
9 is a perfect square and divides 373248
16 is a perfect square and divides 373248
36 is a perfect square and divides 373248
64 is a perfect square and divides 373248
81 is a perfect square and divides 373248
144 is a perfect square and divides 373248
256 is a perfect square and divides 373248
324 is a perfect square and divides 373248
576 is a perfect square and divides 373248
729 is a perfect square and divides 373248
1296 is a perfect square and divides 373248
2304 is a perfect square and divides 373248
2916 is a perfect square and divides 373248
5184 is a perfect square and divides 373248
11664 is a perfect square and divides 373248
20736 is a perfect square and divides 373248
46656 is a perfect square and divides 373248
186624 is a perfect square and divides 373248
Step 3: Divide To Perfect Square
Divide 373248 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 373248 in its simplest form: 432√2
How do you simplify √373248
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 373248. Divide 373248 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 432√2.
Simplified Decimal Form of √373248
The square root of 373248 is approximately 610.94 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √31 | Square root of 31 is the simplest radical form. | √31 |
| √13 | Square root of 13 is the simplest radical form. | √13 |
| √90 | 3√10 | √2 x √3 x √3 x √5 |
| √646 | Square root of 646 is the simplest radical form. | √2 x √17 x √19 |
| √304 | 4√19 | √2 x √2 x √2 x √2 x √19 |
| √791 | Square root of 791 is the simplest radical form. | √7 x √113 |
| √2564 | 2√641 | √2 x √2 x √641 |
| √4144 | 4√259 | √2 x √2 x √2 x √2 x √7 x √37 |
| √5128 | 2√1282 | √2 x √2 x √2 x √641 |