Square Root Of 38416 In Simplest Radical Form
Simplify the square root of 38416 to its lowest radical form.ANSWER: 196√1
196√1 is in the lowest radical form.
Simplified Radical Form of √38416
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 √38416, we need to divide into factors.
√38416 = √2 x √2 x √2 x √2 x √7 x √7 x √7 x √7Step 2: List Perfect Squares
1 is a perfect square and divides 38416
4 is a perfect square and divides 38416
16 is a perfect square and divides 38416
49 is a perfect square and divides 38416
196 is a perfect square and divides 38416
784 is a perfect square and divides 38416
2401 is a perfect square and divides 38416
9604 is a perfect square and divides 38416
38416 is a perfect square and divides 38416
Step 3: Divide To Perfect Square
Divide 38416 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 38416 in its simplest form: 196√1
How do you simplify √38416
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 38416. Divide 38416 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 196√1.
Simplified Decimal Form of √38416
The square root of 38416 is approximately 196 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √39 | Square root of 39 is the simplest radical form. | √3 x √13 |
| √5 | Square root of 5 is the simplest radical form. | √5 |
| √8 | 2√2 | √2 x √2 x √2 |
| √787 | Square root of 787 is the simplest radical form. | √787 |
| √389 | Square root of 389 is the simplest radical form. | √389 |
| √343 | 7√7 | √7 x √7 x √7 |
| √1726 | Square root of 1726 is the simplest radical form. | √2 x √863 |
| √1964 | 2√491 | √2 x √2 x √491 |
| √6422 | 13√38 | √2 x √13 x √13 x √19 |