Square Root Of 438976 In Simplest Radical Form
Simplify the square root of 438976 to its lowest radical form.ANSWER: 152√19
152√19 is in the lowest radical form.
Simplified Radical Form of √438976
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 √438976, we need to divide into factors.
√438976 = √2 x √2 x √2 x √2 x √2 x √2 x √19 x √19 x √19Step 2: List Perfect Squares
1 is a perfect square and divides 438976
4 is a perfect square and divides 438976
16 is a perfect square and divides 438976
64 is a perfect square and divides 438976
361 is a perfect square and divides 438976
1444 is a perfect square and divides 438976
5776 is a perfect square and divides 438976
23104 is a perfect square and divides 438976
Step 3: Divide To Perfect Square
Divide 438976 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 438976 in its simplest form: 152√19
How do you simplify √438976
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 438976. Divide 438976 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 152√19.
Simplified Decimal Form of √438976
The square root of 438976 is approximately 662.553 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √16 | 4√1 | √2 x √2 x √2 x √2 |
| √71 | Square root of 71 is the simplest radical form. | √71 |
| √38 | Square root of 38 is the simplest radical form. | √2 x √19 |
| √310 | Square root of 310 is the simplest radical form. | √2 x √5 x √31 |
| √898 | Square root of 898 is the simplest radical form. | √2 x √449 |
| √836 | 2√209 | √2 x √2 x √11 x √19 |
| √7256 | 2√1814 | √2 x √2 x √2 x √907 |
| √8402 | Square root of 8402 is the simplest radical form. | √2 x √4201 |
| √6005 | Square root of 6005 is the simplest radical form. | √5 x √1201 |