Square Root Of 234256 In Simplest Radical Form
Simplify the square root of 234256 to its lowest radical form.ANSWER: 484√1
484√1 is in the lowest radical form.
Simplified Radical Form of √234256
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 √234256, we need to divide into factors.
√234256 = √2 x √2 x √2 x √2 x √11 x √11 x √11 x √11Step 2: List Perfect Squares
1 is a perfect square and divides 234256
4 is a perfect square and divides 234256
16 is a perfect square and divides 234256
121 is a perfect square and divides 234256
484 is a perfect square and divides 234256
1936 is a perfect square and divides 234256
14641 is a perfect square and divides 234256
58564 is a perfect square and divides 234256
234256 is a perfect square and divides 234256
Step 3: Divide To Perfect Square
Divide 234256 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 234256 in its simplest form: 484√1
How do you simplify √234256
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 234256. Divide 234256 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 484√1.
Simplified Decimal Form of √234256
The square root of 234256 is approximately 484 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √14 | Square root of 14 is the simplest radical form. | √2 x √7 |
| √33 | Square root of 33 is the simplest radical form. | √3 x √11 |
| √55 | Square root of 55 is the simplest radical form. | √5 x √11 |
| √212 | 2√53 | √2 x √2 x √53 |
| √353 | Square root of 353 is the simplest radical form. | √353 |
| √478 | Square root of 478 is the simplest radical form. | √2 x √239 |
| √7435 | Square root of 7435 is the simplest radical form. | √5 x √1487 |
| √2758 | Square root of 2758 is the simplest radical form. | √2 x √7 x √197 |
| √8125 | 25√13 | √5 x √5 x √5 x √5 x √13 |