Square Root Of 287496 In Simplest Radical Form
Simplify the square root of 287496 to its lowest radical form.ANSWER: 66√66
66√66 is in the lowest radical form.
Simplified Radical Form of √287496
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 √287496, we need to divide into factors.
√287496 = √2 x √2 x √2 x √3 x √3 x √3 x √11 x √11 x √11Step 2: List Perfect Squares
1 is a perfect square and divides 287496
4 is a perfect square and divides 287496
9 is a perfect square and divides 287496
36 is a perfect square and divides 287496
121 is a perfect square and divides 287496
484 is a perfect square and divides 287496
1089 is a perfect square and divides 287496
4356 is a perfect square and divides 287496
Step 3: Divide To Perfect Square
Divide 287496 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 287496 in its simplest form: 66√66
How do you simplify √287496
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 287496. Divide 287496 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 66√66.
Simplified Decimal Form of √287496
The square root of 287496 is approximately 536.187 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √60 | 2√15 | √2 x √2 x √3 x √5 |
| √45 | 3√5 | √3 x √3 x √5 |
| √94 | Square root of 94 is the simplest radical form. | √2 x √47 |
| √916 | 2√229 | √2 x √2 x √229 |
| √376 | 2√94 | √2 x √2 x √2 x √47 |
| √898 | Square root of 898 is the simplest radical form. | √2 x √449 |
| √1257 | Square root of 1257 is the simplest radical form. | √3 x √419 |
| √9527 | Square root of 9527 is the simplest radical form. | √7 x √1361 |
| √2393 | Square root of 2393 is the simplest radical form. | √2393 |