Square Root Of 778688 In Simplest Radical Form
Simplify the square root of 778688 to its lowest radical form.ANSWER: 184√23
184√23 is in the lowest radical form.
Simplified Radical Form of √778688
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 √778688, we need to divide into factors.
√778688 = √2 x √2 x √2 x √2 x √2 x √2 x √23 x √23 x √23Step 2: List Perfect Squares
1 is a perfect square and divides 778688
4 is a perfect square and divides 778688
16 is a perfect square and divides 778688
64 is a perfect square and divides 778688
529 is a perfect square and divides 778688
2116 is a perfect square and divides 778688
8464 is a perfect square and divides 778688
33856 is a perfect square and divides 778688
Step 3: Divide To Perfect Square
Divide 778688 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 778688 in its simplest form: 184√23
How do you simplify √778688
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 778688. Divide 778688 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 184√23.
Simplified Decimal Form of √778688
The square root of 778688 is approximately 882.433 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √89 | Square root of 89 is the simplest radical form. | √89 |
| √29 | Square root of 29 is the simplest radical form. | √29 |
| √16 | 4√1 | √2 x √2 x √2 x √2 |
| √674 | Square root of 674 is the simplest radical form. | √2 x √337 |
| √851 | Square root of 851 is the simplest radical form. | √23 x √37 |
| √227 | Square root of 227 is the simplest radical form. | √227 |
| √7784 | 2√1946 | √2 x √2 x √2 x √7 x √139 |
| √2322 | 3√258 | √2 x √3 x √3 x √3 x √43 |
| √5783 | Square root of 5783 is the simplest radical form. | √5783 |