Square Root Of 2916 In Simplest Radical Form
Simplify the square root of 2916 to its lowest radical form.ANSWER: 54√1
54√1 is in the lowest radical form.
Simplified Radical Form of √2916
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 √2916, we need to divide into factors.
√2916 = √2 x √2 x √3 x √3 x √3 x √3 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 2916
4 is a perfect square and divides 2916
9 is a perfect square and divides 2916
36 is a perfect square and divides 2916
81 is a perfect square and divides 2916
324 is a perfect square and divides 2916
729 is a perfect square and divides 2916
2916 is a perfect square and divides 2916
Step 3: Divide To Perfect Square
Divide 2916 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 2916 in its simplest form: 54√1
How do you simplify √2916
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 2916. Divide 2916 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 54√1.
Simplified Decimal Form of √2916
The square root of 2916 is approximately 54 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √28 | 2√7 | √2 x √2 x √7 |
| √17 | Square root of 17 is the simplest radical form. | √17 |
| √17 | Square root of 17 is the simplest radical form. | √17 |
| √508 | 2√127 | √2 x √2 x √127 |
| √231 | Square root of 231 is the simplest radical form. | √3 x √7 x √11 |
| √654 | Square root of 654 is the simplest radical form. | √2 x √3 x √109 |
| √9856 | 8√154 | √2 x √2 x √2 x √2 x √2 x √2 x √2 x √7 x √11 |
| √7508 | 2√1877 | √2 x √2 x √1877 |
| √9903 | Square root of 9903 is the simplest radical form. | √3 x √3301 |