Square Root Of 68574961 In Simplest Radical Form
Simplify the square root of 68574961 to its lowest radical form.ANSWER: 8281√1
8281√1 is in the lowest radical form.
Simplified Radical Form of √68574961
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 √68574961, we need to divide into factors.
√68574961 = √7 x √7 x √7 x √7 x √13 x √13 x √13 x √13Step 2: List Perfect Squares
1 is a perfect square and divides 68574961
49 is a perfect square and divides 68574961
169 is a perfect square and divides 68574961
2401 is a perfect square and divides 68574961
8281 is a perfect square and divides 68574961
28561 is a perfect square and divides 68574961
405769 is a perfect square and divides 68574961
1399489 is a perfect square and divides 68574961
68574961 is a perfect square and divides 68574961
Step 3: Divide To Perfect Square
Divide 68574961 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 68574961 in its simplest form: 8281√1
How do you simplify √68574961
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 68574961. Divide 68574961 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 8281√1.
Simplified Decimal Form of √68574961
The square root of 68574961 is approximately 8281 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √68 | 2√17 | √2 x √2 x √17 |
| √64 | 8√1 | √2 x √2 x √2 x √2 x √2 x √2 |
| √91 | Square root of 91 is the simplest radical form. | √7 x √13 |
| √484 | 22√1 | √2 x √2 x √11 x √11 |
| √412 | 2√103 | √2 x √2 x √103 |
| √970 | Square root of 970 is the simplest radical form. | √2 x √5 x √97 |
| √1591 | Square root of 1591 is the simplest radical form. | √37 x √43 |
| √8128 | 8√127 | √2 x √2 x √2 x √2 x √2 x √2 x √127 |
| √6341 | Square root of 6341 is the simplest radical form. | √17 x √373 |