Square Root Of 110592 In Simplest Radical Form
Simplify the square root of 110592 to its lowest radical form.ANSWER: 192√3
192√3 is in the lowest radical form.
Simplified Radical Form of √110592
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 √110592, we need to divide into factors.
√110592 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 110592
4 is a perfect square and divides 110592
9 is a perfect square and divides 110592
16 is a perfect square and divides 110592
36 is a perfect square and divides 110592
64 is a perfect square and divides 110592
144 is a perfect square and divides 110592
256 is a perfect square and divides 110592
576 is a perfect square and divides 110592
1024 is a perfect square and divides 110592
2304 is a perfect square and divides 110592
4096 is a perfect square and divides 110592
9216 is a perfect square and divides 110592
36864 is a perfect square and divides 110592
Step 3: Divide To Perfect Square
Divide 110592 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 110592 in its simplest form: 192√3
How do you simplify √110592
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 110592. Divide 110592 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 192√3.
Simplified Decimal Form of √110592
The square root of 110592 is approximately 332.554 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √15 | Square root of 15 is the simplest radical form. | √3 x √5 |
| √80 | 4√5 | √2 x √2 x √2 x √2 x √5 |
| √11 | Square root of 11 is the simplest radical form. | √11 |
| √361 | 19√1 | √19 x √19 |
| √895 | Square root of 895 is the simplest radical form. | √5 x √179 |
| √529 | 23√1 | √23 x √23 |
| √3094 | Square root of 3094 is the simplest radical form. | √2 x √7 x √13 x √17 |
| √3718 | 13√22 | √2 x √11 x √13 x √13 |
| √9298 | Square root of 9298 is the simplest radical form. | √2 x √4649 |