Square Root Of 85184 In Simplest Radical Form
Simplify the square root of 85184 to its lowest radical form.ANSWER: 88√11
88√11 is in the lowest radical form.
Simplified Radical Form of √85184
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 √85184, we need to divide into factors.
√85184 = √2 x √2 x √2 x √2 x √2 x √2 x √11 x √11 x √11Step 2: List Perfect Squares
1 is a perfect square and divides 85184
4 is a perfect square and divides 85184
16 is a perfect square and divides 85184
64 is a perfect square and divides 85184
121 is a perfect square and divides 85184
484 is a perfect square and divides 85184
1936 is a perfect square and divides 85184
7744 is a perfect square and divides 85184
Step 3: Divide To Perfect Square
Divide 85184 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 85184 in its simplest form: 88√11
How do you simplify √85184
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 85184. Divide 85184 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 88√11.
Simplified Decimal Form of √85184
The square root of 85184 is approximately 291.863 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √75 | 5√3 | √3 x √5 x √5 |
| √70 | Square root of 70 is the simplest radical form. | √2 x √5 x √7 |
| √79 | Square root of 79 is the simplest radical form. | √79 |
| √876 | 2√219 | √2 x √2 x √3 x √73 |
| √697 | Square root of 697 is the simplest radical form. | √17 x √41 |
| √216 | 6√6 | √2 x √2 x √2 x √3 x √3 x √3 |
| √6678 | 3√742 | √2 x √3 x √3 x √7 x √53 |
| √4678 | Square root of 4678 is the simplest radical form. | √2 x √2339 |
| √7997 | Square root of 7997 is the simplest radical form. | √11 x √727 |