Square Root Of 4608 In Simplest Radical Form
Simplify the square root of 4608 to its lowest radical form.ANSWER: 48√2
48√2 is in the lowest radical form.
Simplified Radical Form of √4608
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 √4608, we need to divide into factors.
√4608 = √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √2 x √3 x √3Step 2: List Perfect Squares
1 is a perfect square and divides 4608
4 is a perfect square and divides 4608
9 is a perfect square and divides 4608
16 is a perfect square and divides 4608
36 is a perfect square and divides 4608
64 is a perfect square and divides 4608
144 is a perfect square and divides 4608
256 is a perfect square and divides 4608
576 is a perfect square and divides 4608
2304 is a perfect square and divides 4608
Step 3: Divide To Perfect Square
Divide 4608 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 4608 in its simplest form: 48√2
How do you simplify √4608
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 4608. Divide 4608 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 48√2.
Simplified Decimal Form of √4608
The square root of 4608 is approximately 67.882 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √73 | Square root of 73 is the simplest radical form. | √73 |
| √9 | 3√1 | √3 x √3 |
| √45 | 3√5 | √3 x √3 x √5 |
| √109 | Square root of 109 is the simplest radical form. | √109 |
| √747 | 3√83 | √3 x √3 x √83 |
| √193 | Square root of 193 is the simplest radical form. | √193 |
| √7400 | 10√74 | √2 x √2 x √2 x √5 x √5 x √37 |
| √2396 | 2√599 | √2 x √2 x √599 |
| √6045 | Square root of 6045 is the simplest radical form. | √3 x √5 x √13 x √31 |