Square Root Of 970299 In Simplest Radical Form
Simplify the square root of 970299 to its lowest radical form.ANSWER: 297√11
297√11 is in the lowest radical form.
Simplified Radical Form of √970299
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 √970299, we need to divide into factors.
√970299 = √3 x √3 x √3 x √3 x √3 x √3 x √11 x √11 x √11Step 2: List Perfect Squares
1 is a perfect square and divides 970299
9 is a perfect square and divides 970299
81 is a perfect square and divides 970299
121 is a perfect square and divides 970299
729 is a perfect square and divides 970299
1089 is a perfect square and divides 970299
9801 is a perfect square and divides 970299
88209 is a perfect square and divides 970299
Step 3: Divide To Perfect Square
Divide 970299 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 970299 in its simplest form: 297√11
How do you simplify √970299
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 970299. Divide 970299 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 297√11.
Simplified Decimal Form of √970299
The square root of 970299 is approximately 985.038 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √10 | Square root of 10 is the simplest radical form. | √2 x √5 |
| √72 | 6√2 | √2 x √2 x √2 x √3 x √3 |
| √66 | Square root of 66 is the simplest radical form. | √2 x √3 x √11 |
| √551 | Square root of 551 is the simplest radical form. | √19 x √29 |
| √512 | 16√2 | √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 |
| √406 | Square root of 406 is the simplest radical form. | √2 x √7 x √29 |
| √1712 | 4√107 | √2 x √2 x √2 x √2 x √107 |
| √3046 | Square root of 3046 is the simplest radical form. | √2 x √1523 |
| √5471 | Square root of 5471 is the simplest radical form. | √5471 |