Square Root Of 9834496 In Simplest Radical Form
Simplify the square root of 9834496 to its lowest radical form.ANSWER: 3136√1
3136√1 is in the lowest radical form.
Simplified Radical Form of √9834496
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 √9834496, we need to divide into factors.
√9834496 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √7 x √7 x √7 x √7Step 2: List Perfect Squares
1 is a perfect square and divides 9834496
4 is a perfect square and divides 9834496
16 is a perfect square and divides 9834496
49 is a perfect square and divides 9834496
64 is a perfect square and divides 9834496
196 is a perfect square and divides 9834496
256 is a perfect square and divides 9834496
784 is a perfect square and divides 9834496
1024 is a perfect square and divides 9834496
2401 is a perfect square and divides 9834496
3136 is a perfect square and divides 9834496
4096 is a perfect square and divides 9834496
9604 is a perfect square and divides 9834496
12544 is a perfect square and divides 9834496
38416 is a perfect square and divides 9834496
50176 is a perfect square and divides 9834496
153664 is a perfect square and divides 9834496
200704 is a perfect square and divides 9834496
614656 is a perfect square and divides 9834496
2458624 is a perfect square and divides 9834496
9834496 is a perfect square and divides 9834496
Step 3: Divide To Perfect Square
Divide 9834496 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 9834496 in its simplest form: 3136√1
How do you simplify √9834496
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 9834496. Divide 9834496 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 3136√1.
Simplified Decimal Form of √9834496
The square root of 9834496 is approximately 3136 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √18 | 3√2 | √2 x √3 x √3 |
| √44 | 2√11 | √2 x √2 x √11 |
| √35 | Square root of 35 is the simplest radical form. | √5 x √7 |
| √759 | Square root of 759 is the simplest radical form. | √3 x √11 x √23 |
| √298 | Square root of 298 is the simplest radical form. | √2 x √149 |
| √213 | Square root of 213 is the simplest radical form. | √3 x √71 |
| √1100 | 10√11 | √2 x √2 x √5 x √5 x √11 |
| √3427 | Square root of 3427 is the simplest radical form. | √23 x √149 |
| √6234 | Square root of 6234 is the simplest radical form. | √2 x √3 x √1039 |