Square Root Of 4352 In Simplest Radical Form
Simplify the square root of 4352 to its lowest radical form.ANSWER: 16√17
16√17 is in the lowest radical form.
Simplified Radical Form of √4352
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 √4352, we need to divide into factors.
√4352 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √17Step 2: List Perfect Squares
1 is a perfect square and divides 4352
4 is a perfect square and divides 4352
16 is a perfect square and divides 4352
64 is a perfect square and divides 4352
256 is a perfect square and divides 4352
Step 3: Divide To Perfect Square
Divide 4352 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 4352 in its simplest form: 16√17
How do you simplify √4352
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 4352. Divide 4352 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 16√17.
Simplified Decimal Form of √4352
The square root of 4352 is approximately 65.97 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √55 | Square root of 55 is the simplest radical form. | √5 x √11 |
| √14 | Square root of 14 is the simplest radical form. | √2 x √7 |
| √70 | Square root of 70 is the simplest radical form. | √2 x √5 x √7 |
| √126 | 3√14 | √2 x √3 x √3 x √7 |
| √539 | 7√11 | √7 x √7 x √11 |
| √384 | 8√6 | √2 x √2 x √2 x √2 x √2 x √2 x √2 x √3 |
| √1923 | Square root of 1923 is the simplest radical form. | √3 x √641 |
| √8471 | Square root of 8471 is the simplest radical form. | √43 x √197 |
| √2068 | 2√517 | √2 x √2 x √11 x √47 |