Square Root Of 7776 In Simplest Radical Form
Simplify the square root of 7776 to its lowest radical form.ANSWER: 36√6
36√6 is in the lowest radical form.
Simplified Radical Form of √7776
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 √7776, we need to divide into factors.
√7776 = √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 7776
4 is a perfect square and divides 7776
9 is a perfect square and divides 7776
16 is a perfect square and divides 7776
36 is a perfect square and divides 7776
81 is a perfect square and divides 7776
144 is a perfect square and divides 7776
324 is a perfect square and divides 7776
1296 is a perfect square and divides 7776
Step 3: Divide To Perfect Square
Divide 7776 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 7776 in its simplest form: 36√6
How do you simplify √7776
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 7776. Divide 7776 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 36√6.
Simplified Decimal Form of √7776
The square root of 7776 is approximately 88.182 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √89 | Square root of 89 is the simplest radical form. | √89 |
| √72 | 6√2 | √2 x √2 x √2 x √3 x √3 |
| √74 | Square root of 74 is the simplest radical form. | √2 x √37 |
| √344 | 2√86 | √2 x √2 x √2 x √43 |
| √160 | 4√10 | √2 x √2 x √2 x √2 x √2 x √5 |
| √209 | Square root of 209 is the simplest radical form. | √11 x √19 |
| √6197 | Square root of 6197 is the simplest radical form. | √6197 |
| √6443 | Square root of 6443 is the simplest radical form. | √17 x √379 |
| √2121 | Square root of 2121 is the simplest radical form. | √3 x √7 x √101 |