Square Root Of 84934656 In Simplest Radical Form
Simplify the square root of 84934656 to its lowest radical form.ANSWER: 9216√1
9216√1 is in the lowest radical form.
Simplified Radical Form of √84934656
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 √84934656, we need to divide into factors.
√84934656 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √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 √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 84934656
4 is a perfect square and divides 84934656
9 is a perfect square and divides 84934656
16 is a perfect square and divides 84934656
36 is a perfect square and divides 84934656
64 is a perfect square and divides 84934656
81 is a perfect square and divides 84934656
144 is a perfect square and divides 84934656
256 is a perfect square and divides 84934656
324 is a perfect square and divides 84934656
576 is a perfect square and divides 84934656
1024 is a perfect square and divides 84934656
1296 is a perfect square and divides 84934656
2304 is a perfect square and divides 84934656
4096 is a perfect square and divides 84934656
5184 is a perfect square and divides 84934656
9216 is a perfect square and divides 84934656
16384 is a perfect square and divides 84934656
20736 is a perfect square and divides 84934656
36864 is a perfect square and divides 84934656
65536 is a perfect square and divides 84934656
82944 is a perfect square and divides 84934656
147456 is a perfect square and divides 84934656
262144 is a perfect square and divides 84934656
331776 is a perfect square and divides 84934656
589824 is a perfect square and divides 84934656
1048576 is a perfect square and divides 84934656
1327104 is a perfect square and divides 84934656
2359296 is a perfect square and divides 84934656
5308416 is a perfect square and divides 84934656
9437184 is a perfect square and divides 84934656
21233664 is a perfect square and divides 84934656
84934656 is a perfect square and divides 84934656
Step 3: Divide To Perfect Square
Divide 84934656 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 84934656 in its simplest form: 9216√1
How do you simplify √84934656
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 84934656. Divide 84934656 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 9216√1.
Simplified Decimal Form of √84934656
The square root of 84934656 is approximately 9216 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √47 | Square root of 47 is the simplest radical form. | √47 |
| √83 | Square root of 83 is the simplest radical form. | √83 |
| √27 | 3√3 | √3 x √3 x √3 |
| √107 | Square root of 107 is the simplest radical form. | √107 |
| √354 | Square root of 354 is the simplest radical form. | √2 x √3 x √59 |
| √489 | Square root of 489 is the simplest radical form. | √3 x √163 |
| √1859 | 13√11 | √11 x √13 x √13 |
| √7405 | Square root of 7405 is the simplest radical form. | √5 x √1481 |
| √8686 | Square root of 8686 is the simplest radical form. | √2 x √43 x √101 |