Square Root Of 92236816 In Simplest Radical Form
Simplify the square root of 92236816 to its lowest radical form.ANSWER: 9604√1
9604√1 is in the lowest radical form.
Simplified Radical Form of √92236816
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 √92236816, we need to divide into factors.
√92236816 = √2 x √2 x √2 x √2 x √7 x √7 x √7 x √7 x √7 x √7 x √7 x √7Step 2: List Perfect Squares
1 is a perfect square and divides 92236816
4 is a perfect square and divides 92236816
16 is a perfect square and divides 92236816
49 is a perfect square and divides 92236816
196 is a perfect square and divides 92236816
784 is a perfect square and divides 92236816
2401 is a perfect square and divides 92236816
9604 is a perfect square and divides 92236816
38416 is a perfect square and divides 92236816
117649 is a perfect square and divides 92236816
470596 is a perfect square and divides 92236816
1882384 is a perfect square and divides 92236816
5764801 is a perfect square and divides 92236816
23059204 is a perfect square and divides 92236816
92236816 is a perfect square and divides 92236816
Step 3: Divide To Perfect Square
Divide 92236816 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 92236816 in its simplest form: 9604√1
How do you simplify √92236816
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 92236816. Divide 92236816 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 9604√1.
Simplified Decimal Form of √92236816
The square root of 92236816 is approximately 9604 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √21 | Square root of 21 is the simplest radical form. | √3 x √7 |
| √89 | Square root of 89 is the simplest radical form. | √89 |
| √22 | Square root of 22 is the simplest radical form. | √2 x √11 |
| √238 | Square root of 238 is the simplest radical form. | √2 x √7 x √17 |
| √748 | 2√187 | √2 x √2 x √11 x √17 |
| √519 | Square root of 519 is the simplest radical form. | √3 x √173 |
| √8967 | 7√183 | √3 x √7 x √7 x √61 |
| √2580 | 2√645 | √2 x √2 x √3 x √5 x √43 |
| √8162 | Square root of 8162 is the simplest radical form. | √2 x √7 x √11 x √53 |