Square Root Of 5308416 In Simplest Radical Form
Simplify the square root of 5308416 to its lowest radical form.ANSWER: 2304√1
2304√1 is in the lowest radical form.
Simplified Radical Form of √5308416
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 √5308416, we need to divide into factors.
√5308416 = √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 5308416
4 is a perfect square and divides 5308416
9 is a perfect square and divides 5308416
16 is a perfect square and divides 5308416
36 is a perfect square and divides 5308416
64 is a perfect square and divides 5308416
81 is a perfect square and divides 5308416
144 is a perfect square and divides 5308416
256 is a perfect square and divides 5308416
324 is a perfect square and divides 5308416
576 is a perfect square and divides 5308416
1024 is a perfect square and divides 5308416
1296 is a perfect square and divides 5308416
2304 is a perfect square and divides 5308416
4096 is a perfect square and divides 5308416
5184 is a perfect square and divides 5308416
9216 is a perfect square and divides 5308416
16384 is a perfect square and divides 5308416
20736 is a perfect square and divides 5308416
36864 is a perfect square and divides 5308416
65536 is a perfect square and divides 5308416
82944 is a perfect square and divides 5308416
147456 is a perfect square and divides 5308416
331776 is a perfect square and divides 5308416
589824 is a perfect square and divides 5308416
1327104 is a perfect square and divides 5308416
5308416 is a perfect square and divides 5308416
Step 3: Divide To Perfect Square
Divide 5308416 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 5308416 in its simplest form: 2304√1
How do you simplify √5308416
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 5308416. Divide 5308416 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 2304√1.
Simplified Decimal Form of √5308416
The square root of 5308416 is approximately 2304 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √54 | 3√6 | √2 x √3 x √3 x √3 |
| √33 | Square root of 33 is the simplest radical form. | √3 x √11 |
| √32 | 4√2 | √2 x √2 x √2 x √2 x √2 |
| √738 | 3√82 | √2 x √3 x √3 x √41 |
| √630 | 3√70 | √2 x √3 x √3 x √5 x √7 |
| √530 | Square root of 530 is the simplest radical form. | √2 x √5 x √53 |
| √3337 | Square root of 3337 is the simplest radical form. | √47 x √71 |
| √8484 | 2√2121 | √2 x √2 x √3 x √7 x √101 |
| √5378 | Square root of 5378 is the simplest radical form. | √2 x √2689 |