Square Root Of 5184 In Simplest Radical Form
Simplify the square root of 5184 to its lowest radical form.ANSWER: 72√1
72√1 is in the lowest radical form.
Simplified Radical Form of √5184
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 √5184, we need to divide into factors.
√5184 = √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 5184
4 is a perfect square and divides 5184
9 is a perfect square and divides 5184
16 is a perfect square and divides 5184
36 is a perfect square and divides 5184
64 is a perfect square and divides 5184
81 is a perfect square and divides 5184
144 is a perfect square and divides 5184
324 is a perfect square and divides 5184
576 is a perfect square and divides 5184
1296 is a perfect square and divides 5184
5184 is a perfect square and divides 5184
Step 3: Divide To Perfect Square
Divide 5184 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 5184 in its simplest form: 72√1
How do you simplify √5184
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 5184. Divide 5184 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 72√1.
Simplified Decimal Form of √5184
The square root of 5184 is approximately 72 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √41 | Square root of 41 is the simplest radical form. | √41 |
| √42 | Square root of 42 is the simplest radical form. | √2 x √3 x √7 |
| √84 | 2√21 | √2 x √2 x √3 x √7 |
| √342 | 3√38 | √2 x √3 x √3 x √19 |
| √316 | 2√79 | √2 x √2 x √79 |
| √154 | Square root of 154 is the simplest radical form. | √2 x √7 x √11 |
| √2199 | Square root of 2199 is the simplest radical form. | √3 x √733 |
| √9248 | 68√2 | √2 x √2 x √2 x √2 x √2 x √17 x √17 |
| √3909 | Square root of 3909 is the simplest radical form. | √3 x √1303 |